Wikipǣdia angwiki https://ang.wikipedia.org/wiki/Heafodtramet MediaWiki 1.47.0-wmf.21 first-letter Media Syndrig Mōtung Brūcend Brūcendmōtung Wikipǣdia Wikipǣdiamōtung Ymele Ymelmōtung MediaWiki MediaWikimōtung Bysen Bysenmōtung Help Helpmōtung Flocc Floccmōtung TimedText TimedText talk Module Module talk Event Event talk 0 747 232072 227976 2026-09-25T20:26:01Z ~2026-51859-23 142958 /* */ Updated chancellor 232072 wikitext text/x-wiki {{Cyþþubox land |ænglisc fullnama = Ēastrīċe seo Cynewise |nama = Ēastrīċe |agenspræce fullnama = Republik Österreich |biliþ = |biliþ gewrit = |fana = Flag_of_Austria.svg |fana gewrit = [[Æastrices Fana]] |scild = Coat_of_arms_of_Austria.svg |scild gewrit = [[Æastrices rices wæpnas]] |cwide = |ænglisc cwide = |anstefn = Land der Berge, Land am Strome |ænglisc anstefn = Land Beorga, Land on þære Æa |landscite = Austria in European Union.svg |landscite gewrit= |leodweard = [[Cynewise|Cynewise]] |ambihtlicu spræc= [[Þeodsc spræc]] |folces gereord = |elles gereordas = [[Slofenisc spræc]]<br/>[[Ungrisc spræc]]<ref>{{cite web |url=https://www.demokratiewebstatt.at/thema/sprachen/amtssprachen-in-oesterreich/die-verschiedenen-amtssprachen-in-oesterreich/ |title=Die verschiedenen Amtssprachen in Österreich |website= DemokratieWEBstatt.at |access-date=23 May 2018 |archive-url= https://web.archive.org/web/20180524084441/https://www.demokratiewebstatt.at/thema/sprachen/amtssprachen-in-oesterreich/die-verschiedenen-amtssprachen-in-oesterreich/ |archive-date=24 May 2018 |dead-url=no |df=dmy-all}}</ref><ref>{{cite web |url=http://www.ris.bka.gv.at/Dokument.wxe?Abfrage=Bundesnormen&Dokumentnummer=NOR40066723 |publisher= Rechtsinformationssystem des Bundes |title=Regional Languages of Austria |year=2013 |access-date=27 July 2013 |archive-url= https://web.archive.org/web/20131018115726/http://www.ris.bka.gv.at/Dokument.wxe?Abfrage=Bundesnormen&Dokumentnummer=NOR40066723 |archive-date=18 October 2013 |dead-url=no |df=dmy-all}}</ref> |steall = |heafodstol = [[Uigenna]] |mæste burg = [[Uigenna]] |breges titul = Foresittend |brego = [[Alexander Van der Bellen]] |ealdormannes titul= Forma Þegn |ealdorman = [[Christian Stocker]] |leodweardes heafod= |wyrþingdæg = |bradnes = 83,883 km² |menniscu = {{profit}} 8,978,929<ref name="statistik-population">{{cite web |title=Population by Year-/Quarter-beginning |url=http://www.statistik.at/web_de/statistiken/menschen_und_gesellschaft/bevoelkerung/bevoelkerungsstand_und_veraenderung/bevoelkerung_zu_jahres-_quartalsanfang/023582.html |date=7 November 2018 |access-date=12 June 2015 |archive-url= https://web.archive.org/web/20150612161754/http://www.statistik.at/web_de/statistiken/menschen_und_gesellschaft/bevoelkerung/bevoelkerungsstand_und_veraenderung/bevoelkerung_zu_jahres-_quartalsanfang/023582.html |archive-date=12 June 2015 |dead-url=no |df=dmy-all}}</ref> |þiccnes = 107 buend/km² |geleafan = [[Cristendom]] |GDP getæl = 477.672 mld USD<ref name="imf2">{{cite web |url=http://www.imf.org/external/pubs/ft/weo/2018/01/weodata/weorept.aspx?sy=2017&ey=2020&scsm=1&ssd=1&sort=country&ds=.&br=1&pr1.x=70&pr1.y=9&c=122&s=NGDP_RPCH%2CNGDPD%2CPPPGDP%2CNGDPDPC%2CPPPPC&grp=0&a= |title=Austria |publisher= [[International Monetary Fund]] |date=1 April 2018 |accessdate=23 July 2018}}</ref> |GDP ælcum heafde= 53,764 mld USD<ref name="imf2"/> |landesforþbæro = |feoh = Euro (€) (EUR) |tidgyrdel = +1 |tidgyrdel 2 = +2 |sundorricehad = |webbnamena tægl = .at |feorspræcan forerim = +43 |wægnplatung = AT |hēafodstōl=[[Uigenna]]}} '''Ēastrīċe seo Cynewise''' ({{lang-de|Republik Österreich}}) is [[sæstrandleas]] land in [[Middel Europe|Middelre Europan]]. Hit is [[motlic þringgeweald|motlic þringgeweald]]<!-- parliamentary democracy -->. Ēastrīċe hæfþ gebeon agylda þara [[Geandu Leodricu|Geandena Leodrica]]<!-- UN --> siþþan þæm [[1955 gear]]e, and þære [[Europisc Gesamnung|Europiscan Gesamnunge]] siþþan þæm [[1995 gear]]e. Hit ligþ be [[Þeodiscland]]e and [[Cecland]]e benorðan him, [[Slofacia|Slofacie]] and [[Ungerland]]e beeastan him, [[Slofenia|Slofenie]] and [[Italia|Italie]] besuðan him, and [[Swissland]]e and [[Leohtenstan]]e bewestan him. == Stær == Æfter þe gehiersumode þis land [[Lædenware]], [[Hunas]], [[Langbeardas]], [[Gotan#Æastgotan|Æastgotan]], [[Bægwaraland|Bægware]] and [[Francan]], wæs Ēastrīċe geweald fram þæm [[Babenbeorg]]es rice fram þæm [[teoðe hundgear|teoðan hundgeara]] oð þæt [[þreoteoðe hundgear]]e. Æfter þæt Babenbeorges hus afylgode þa [[Habsburg]]as, þæs hus ricsode Ēastrīċe oþ þæt [[1918 gear]]. Æfter þære adilegiunge þæs [[Halig Romanisc Rice|Halgan Romaniscan Rices]] on þæm [[1806 geare]], '''Ēastrīċes Casererice''' ({{Lang-de|Kaisertum Österreich}}) gestaðolode [[Francis II Æasterrice Casere|Francis&nbsp;II]]. On þæm [[1867 gear]]e andwendede Franz-Iosef&nbsp;I Casere þis casererice on [[Ēastrīce-Ungerland]]e þæm twifealdan cynedome. Þæt Casererice wæs adæled on sumu anstandendu ricu æfter þæm unsige þara [[Middele Domas|Middelena Doma]] on þære [[Ǣrest Woruldguþ|Ǣrestan Uoruldguðe]], þe worhte Ēastrīċe swa hit is todæg. In þæm [[1918]] geare wearþ Ēastrīċe [[cynewise|cynewise]], þe gelæstede oþ þæt [[1934 gear]], þa þa [[Engelbert Dollfuß]] Canceler staðolode tictatorscipe cwæl. Ēastrīċe wæs be [[Æðelwulf Hitler|Æðelwulfe Hitlere]] befangen for Þeodisclande, on þæm [[1938 gear]]e (seoh þæt gewrit be [[Þeodnes]]se). Hitler wæs self on Æastricþeode geboren. Æfter þære oferdrifunge þara Nazea, þa [[Geræd in Potsdame|Geferan gesetedon Æastrice]] fram þæm ende þære [[Iðru Woruldguþ|Iðran Uoruldguðe]] oþ þæt [[1955 gear]], þa þa þæt land eft wearþ ful anstandende leodaþing under þæm gerade be þæm þe hit belufe ungewæred (''seoh eac:'' [[Æastriclic Rices Næming]]). Huru æfter þæm geafealle [[motscipe]]s on [[Æasterne Europe|Æasternre Europe]], Ēastrīċe wearþ æfre gewyrcendre on Europiscum gelimpungum, and in þæm [[1995 gear]], Ēastrīċe geþoftode wiþ þa [[Europisc Gesamnung|Europiscan Gesamnunge]], and seo [[Euro]] wearþ þæt gestede ricisce feos gemitta on þæm [[1999 gear]]e. == Fruma þæs naman == Se [[Þeodisc spræc|Þeodisca]] nama ''Österreich'' cann wesan understanden samwell in [[Englisc spræc|Englisce]] swa "easterne rice", þe is of [[Eald Þeodisc|Ealdum Þeodisce]] ''[[Ostarrîchi]]''. Se nama gelice wæs staðolod þurh [[leodþeaw]]isce awendunge þæs [[Midieldisc Læden|Midieldisclædnan]] naman to þæm landscipum: ''Marchia orientalis'', þe mænþ "easterne landmearc," for þæm þe hit læg æt þæm easternan oran þæs [[Halig Romanisc Rice|Halgan Romaniscan Rices]]. Care weorðe is hit þæt seo forðung þæs Lædnan naman fram þæm forman Ealdþeodiscan naman worhte þa nytte of "Aust-" swa "east", ær þonne "suþ" swa on [[Eald Læden|Ealdum Lædne]]. == Fruman == <references/> {{Land on Europan|Ēastrīċe}} {{stub}} [[flocc:Niwlicu word]] p2a7494la9b6prlvac2qmi8hlcxdlw5 0 5361 232070 230857 2026-09-25T20:21:27Z ~2026-51859-23 142958 Chamged the president of Hungary to the current, legitimate one 232070 wikitext text/x-wiki {{Cyþþubox rice |nama=Ungerland |agenspræc=Magyarország |biliþ=Budapest_Parlament-2.jpg |biliþ gewrit=Ƿitenagemothus on Budapeste |fana=Flag of Hungary.svg |fana gewrit=Ungerland fāna |scild=Coat of Arms of Hungary.svg |scild gewrit=Ungerland rīces tæcn |landscite=EU-Hungary.svg |ambihtlic spræc= |heafodstol=Budapest |brego=[[:en:András Baka|András Baka]] |breges titul=Foresittend |leodweardes heafod=[[:en:Péter Magyar|Péter Magyar]] |leodweardes heafdes titul=Forma Þegn |bradnes=93,030 km² |menniscu=9,797,561 <small>(2017)</small> |sundorricehad= |wyrþingdæg= |feoh=Forint (HUF) |tidgyrdel=+1 |tidgydel 2=+2 |antefn= |tld=.hu |feorspræcan forerim=+36 }} '''Ungerland''' is in middlum [[Europe|Europan]]. His [[hēafodstōl|hēafodburh]] is [[Budapest]]. {{Land on Europan}} {{stycce}} ncppai3zzlwtnvzku3frpmggj7y55f9 0 26449 232071 223617 2026-09-25T20:23:20Z ~2026-51859-23 142958 /* */ Updated the PM and President 232071 wikitext text/x-wiki {{Cyþþubox land |ænglisc fullnama = Slofacisce Cyneƿīse |nama = Slofacia |agenspræce fullnama = Slovenská republika |biliþ = |biliþ gewrit = |fana = Flag_of_Slovakia.svg |fana gewrit = Fana |scild = Coat_of_arms_of_Slovakia.svg |scild gewrit = Rīces ƿæpnas |cƿide = |ænglisc cƿide = |anstefn = Nad Tatrou sa blýska |ænglisc anstefn = |landscite = Slovakia in European Union.svg |landscite gewrit = |lēodƿeard = Cyneƿīse |ambihtlicu sprǣc = [[Slofacisc sprǣc]] |folces gereord = |elles gereordas = |steall = |hēafodstōl = [[Pressburg]] |mæste burg = |breges titul = Foresittend |brego = [[Peter Pellegrini]] |ealdormannes titul = Forma Þegn |ealdorman = [[Robert Fico]] |lēodweardes hēafod = |wyrþingdæg = |brādnes = 49 035 km² |menniscu = {{profit}} 5,445,802<ref>{{cite web |url=https://slovak.statistics.sk/wps/portal/ext/products/informationmessages/inf_sprava_detail/53574f49-236a-4825-9db7-126a97ca429a/!ut/p/z1/tVO5csIwFPyWFJTiPUuyZZfGAWOugIk51GTE7YBtDo8Jfx95hoaCI0VeI2m0u5q3-wQSJiBTVcRrlcdZqnb6PJXW10AEdq1muIi1DsOg1R72ml6D-pEJ41uA3QvrGHy6fT9scQO5CfLmujaiGIheaLQHA79t8Cvf890mFx1Eu-ObGLjNKHQGjKHLXuPjnXLxNf4DgHzc_wgkyHma7_MNTLPZSW3IaUvidEXUNq-g3mTHRLtZpEty2h9VcalgcVrmW72azBR8xR1CmaUIt6lJnMVMEINayhFzxamjSvn9PF7A9CX0-Fle8rFb4_K9J4E805APPY_EFdAY9qnrcN97Dz8aemY8ag87FkXfegJAA6a6TXG3TUPAuIiXZ4jS0vwdDP_oYhOhBTKeJdXzPKliVdgCmRA2p9yxTMbKb0GPXa-71rIq35R5ZzB5SVtT4-_DQbp6bLI0X_7kMPmPudknka7EZheyDeurbp1xObuc334BX4PlNQ!!/dz/d5/L2dBISEvZ0FBIS9nQSEh/ |title=Stav obyvateľstva v SR k 31. decembru 2018 |website=slovak.statistics.sk |date=31 December 2018}}</ref> |þiccnes = 111/km² |gelēafan = [[Crīstendōm]] |GDP getæl = 109.863 mld USD<ref name="IMFWEOSK">{{cite web |url=https://www.imf.org/external/pubs/ft/weo/2019/01/weodata/weorept.aspx?sy=2017&ey=2020&scsm=1&ssd=1&sort=country&ds=.&br=1&pr1.x=42&pr1.y=18&c=936&s=NGDPD%2CPPPGDP%2CNGDPDPC%2CPPPPC&grp=0&a= |title=World Economic Outlook Database, April 2019 |publisher=[[International Monetary Fund]] |website=IMF.org |access-date=15 May 2019}}</ref> |GDP ǣlcum hēafde = 20,155 USD<ref name="IMFWEOSK"/> |landesforþbæro = |feoh = Euro (€) (EUR) |tidgyrdel = +1 |tidgyrdel 2 = +2 |sundorricehad = |ƿebbnamena tægl = .sk |feorspræcan forerim = +421 |wægnplatung = SK }} '''Slofacland''' ({{lang-sk|Slovensko}}) is land on [[Europe|Europan]]. Hēr spricþ man on [[Slofacisc sprǣc|Slofacisce]]. == Fruman == <references/> == Ūtƿeardlice bendas == * [https://web.archive.org/web/20050528231000/http://www.government.gov.sk/english/ The Slovak Republic Government Office] {{Land on Europan}} 7v20t55wkacc6nygo8kyiskll4ao257 0 28653 232069 2026-09-25T17:26:33Z Rylesbourne 125148 Nīwe tramet: {{Cyþþubox folcstede |nama = {{PAGENAME}} |flocc = [[Hēafodburg|Eardheafodstol]] |biliþ = Langinkoski.jpg |biliþ gewrit = Langincosc on Cottan |rice = {{flag|Finnland}} |underrice = {{flagicon image|Kymenlaakson maakunnan vaakuna.svg}} [[Cymenedele]] }} '''Cotta''' ({{lang-fi|Kotka}}) is burh on [[Finnum]]and þæt rēcedliċe [[heafodstol]] [[Cymenedele]]n. Hēo līþ on þǣm sūþ-ēastran... 232069 wikitext text/x-wiki {{Cyþþubox folcstede |nama = {{PAGENAME}} |flocc = [[Hēafodburg|Eardheafodstol]] |biliþ = Langinkoski.jpg |biliþ gewrit = Langincosc on Cottan |rice = {{flag|Finnland}} |underrice = {{flagicon image|Kymenlaakson maakunnan vaakuna.svg}} [[Cymenedele]] }} '''Cotta''' ({{lang-fi|Kotka}}) is burh on [[Finnum]]and þæt rēcedliċe [[heafodstol]] [[Cymenedele]]n. Hēo līþ on þǣm sūþ-ēastran inlande þæs rīċes. {{stycce}} {{DEFAULTSORT:Cotta}} [[Flocc:Byrig on Finnum]] [[Flocc:Ġemǣnescipes on Cymenedelen]] 41pj7awn9777masi70iadtelb4ikq11 0 28654 232073 2026-09-26T05:06:37Z Ryblow 142974 /* */ Swiss actuary and mathematician specializing in actuarial science and risk modelling 232073 wikitext text/x-wiki {{Short description|Swiss actuary and mathematician}} {{Use dmy dates|date=September 2026}} {{Infobox scientist|name=Mario V. Wüthrich|native_name=Mario Valentin Wüthrich|birth_date={{birth date and age|1969|5|19|df=y}}|nationality=Swiss|fields=[[Actuarial science]], [[probability theory]], [[statistics]], [[machine learning]]|workplaces=[[ETH Zurich]]<br />Winterthur Insurance|alma_mater=[[ETH Zurich]]|thesis_title=Crossing Brownian motion in a soft Poissonian potential|thesis_url=https://doi.org/10.3929/ethz-a-002049781|thesis_year=1999|doctoral_advisor=[[Alain-Sol Sznitman]]|known_for=Stochastic [[loss reserving|claims reserving]]; one-year claims development result; actuarial applications of [[machine learning]]}} '''Mario Valentin Wüthrich''' (born 19 May 1969) is a Swiss [[actuary]] and mathematician whose work lies at the intersection of actuarial mathematics, statistics and quantitative risk modelling. He is a titular professor (adjunct professor) in the Department of Mathematics at [[ETH Zurich]] and Director of Actuarial Studies at RiskLab Switzerland.<ref name="eth-current">{{cite web|title=Mario Wüthrich|url=https://math.ethz.ch/research/insurance-mathematics-stochastic-finance/mario-wuethrich.html|publisher=Department of Mathematics, ETH Zurich|access-date=26 September 2026}}</ref><ref name="risklab-members">{{cite web|title=Members of RiskLab|url=https://risklab.ethz.ch/people/members.html|publisher=RiskLab Switzerland, ETH Zurich|access-date=26 September 2026}}</ref> He has served as Editor-in-Chief of the ''[[ASTIN Bulletin]]'', the journal of the [[International Actuarial Association]], since 2018.<ref name="astin-editor">{{cite journal|last=Wüthrich|first=Mario V.|title=Editorial|journal=ASTIN Bulletin|volume=48|issue=1|pages=1–2|year=2018|doi=10.1017/asb.2017.43}}</ref> Wüthrich is particularly associated with stochastic methods for [[Loss reserving|claims reserving]]. Work with Michael Merz on the one-year ''claims development result'' extended the distribution-free [[chain-ladder method]] to the one-year horizon used in solvency and risk-capital calculations.<ref name="cdr2008">{{cite journal|last1=Merz|first1=Michael|last2=Wüthrich|first2=Mario V.|title=Modelling the claims development result for solvency purposes|journal=Casualty Actuarial Society E-Forum|issue=Fall|pages=542–568|year=2008|url=https://www.casact.org/abstract/modeling-claims-development-result-solvency-purposes}}</ref> Later actuarial literature commonly refers to the resulting construction as the Merz–Wüthrich approach or modification to the Mack model.<ref name="cas-one-year">{{cite web|title=A Practical Way to Estimate One-year Reserve Risk|url=https://www.casact.org/sites/default/files/database/forum_12sumforum_completesummer12.pdf|publisher=Casualty Actuarial Society|year=2012|access-date=26 September 2026}}</ref> From the late 2010s onward, a substantial part of his research has concerned the use, interpretation and regulation of machine-learning models in insurance, including neural-network reserving, mortality forecasting, interpretable deep learning and discrimination-free pricing.<ref name="nn-chain">{{cite journal|last=Wüthrich|first=Mario V.|title=Neural networks applied to chain–ladder reserving|journal=European Actuarial Journal|volume=8|issue=2|pages=407–436|year=2018|doi=10.1007/s13385-018-0184-4}}</ref><ref name="localglm">{{cite journal|last1=Richman|first1=Ronald|last2=Wüthrich|first2=Mario V.|title=LocalGLMnet: interpretable deep learning for tabular data|journal=Scandinavian Actuarial Journal|volume=2023|issue=1|pages=71–95|year=2023|doi=10.1080/03461238.2022.2081816}}</ref> == Early life and education == Wüthrich was born on 19 May 1969.<ref name="thesis">{{cite thesis|last=Wüthrich|first=Mario Valentin|title=Crossing Brownian motion in a soft Poissonian potential|type=Doctoral dissertation|publisher=ETH Zurich|year=1999|doi=10.3929/ethz-a-002049781}}</ref> He studied mathematics at ETH Zurich and received the degree of ''Diplom-Mathematiker'' before continuing to doctoral study there. His 1999 dissertation, ''Crossing Brownian motion in a soft Poissonian potential'', was written under the supervision of [[Alain-Sol Sznitman]], with [[Erwin Bolthausen]] as co-examiner.<ref name="thesis" /> His early research was in probability theory and the mathematical theory of random media. In a series of papers in the late 1990s, he studied the behaviour of [[Brownian motion]] in Poissonian potentials, including fluctuations, geodesics and scaling relations.<ref>{{cite journal|last=Wüthrich|first=Mario V.|title=Fluctuation results for Brownian motion in a Poissonian potential|journal=Annales de l'Institut Henri Poincaré, Probabilités et Statistiques|volume=34|issue=3|pages=279–308|year=1998}}</ref><ref name="scaling">{{cite journal|last=Wüthrich|first=Mario V.|title=Scaling identity for crossing Brownian motion in a Poissonian potential|journal=Probability Theory and Related Fields|volume=112|issue=3|pages=299–319|year=1998|doi=10.1007/s004400050192}}</ref> This work belongs to the study of random environments and directed or crossing paths, rather than to actuarial mathematics, which became the main focus of his later career. == Career == After his doctorate Wüthrich spent a period in academic research before moving into the insurance industry. From 2000 to 2005 he worked at Winterthur Insurance in Switzerland, where his responsibilities included non-life claims reserving and work connected with the development and implementation of the [[Swiss Solvency Test]].<ref name="springer-bio">{{cite book|last=Wüthrich|first=Mario V.|title=Market-Consistent Actuarial Valuation|edition=3rd|series=EAA Series|publisher=Springer|location=Cham|year=2016|doi=10.1007/978-3-319-46636-1|isbn=978-3-319-46635-4}}</ref> He qualified as an Actuary SAA of the Swiss Association of Actuaries in 2004.<ref name="about">{{cite web|title=About|url=https://people.math.ethz.ch/~wueth/about.html|website=Mario Wüthrich, RiskLab, ETH Zurich|access-date=26 September 2026}}</ref> He returned to ETH Zurich in 2005, where he subsequently taught actuarial and financial mathematics and became Director of Actuarial Studies at RiskLab.<ref name="about" /><ref name="risklab-members" /> ETH currently lists him as a ''Titularprofessor'' (adjunct professor) in the Department of Mathematics.<ref name="eth-current" /> His teaching has included courses in non-life insurance mathematics, actuarial data science and market-consistent actuarial valuation.<ref name="eth-teaching">{{cite web|title=Mario Valentin Wüthrich: Course units in Autumn Semester 2026|url=https://www.vvz.ethz.ch/Vorlesungsverzeichnis/dozent.view?ansicht=2&dozide=10017668&lang=en&semkez=2026W|publisher=ETH Zurich|access-date=26 September 2026}}</ref> Wüthrich served on the board of the Swiss Association of Actuaries from 2006 to 2018.<ref name="about" /> He joined the editorial team of the ''ASTIN Bulletin'' before succeeding Andrew Cairns as Editor-in-Chief in 2018.<ref name="astin-editor" /> The International Actuarial Association continues to list him in that position.<ref>{{cite web|title=ASTIN Bulletin|url=https://actuaries.org/publications/astin-bulletin/|publisher=International Actuarial Association|access-date=26 September 2026}}</ref> Since 2025 he has also been Senior Scientific Advisor to insureAI.<ref name="about" /> == Research == === Probability and random media === Wüthrich's doctoral and immediately pre-doctoral research was concerned with Brownian motion in random Poissonian media. His 1998 paper in ''Probability Theory and Related Fields'' established a scaling identity connecting fluctuation exponents for crossing Brownian motion in a Poissonian potential.<ref name="scaling" /> Other work from the same period treated fluctuation bounds, superdiffusive behaviour in two dimensions and geodesics in soft Poissonian potentials.<ref>{{cite journal|last=Wüthrich|first=Mario V.|title=Superdiffusive behavior of two-dimensional Brownian motion in a Poissonian potential|journal=The Annals of Probability|volume=26|issue=3|pages=1000–1015|year=1998}}</ref><ref>{{cite journal|last=Wüthrich|first=Mario V.|title=Geodesics and crossing Brownian motion in a soft Poissonian potential|journal=Annales de l'Institut Henri Poincaré, Probabilités et Statistiques|volume=35|issue=4|pages=509–529|year=1999}}</ref> After completing his doctorate, Wüthrich moved from academic research into the insurance industry. From 2000 to 2005 he worked at Winterthur Insurance, where his work focused on non-life claims reserving and solvency modelling. His later academic research at ETH Zurich developed these topics further, particularly in stochastic reserving, actuarial valuation and statistical modelling for insurance. === Claims reserving === A major strand of Wüthrich's research concerns stochastic modelling of outstanding claims in property and casualty insurance. His 2008 book with Michael Merz, ''Stochastic Claims Reserving Methods in Insurance'', develops stochastic versions of classical reserving techniques and methods for quantifying prediction uncertainty.<ref name="scrm">{{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Stochastic Claims Reserving Methods in Insurance|series=Wiley Finance|publisher=John Wiley & Sons|location=Chichester|year=2008|isbn=978-0-470-72346-3|doi=10.1002/9781119206262}}</ref> Merz and Wüthrich's work on the claims development result focused on the change in an insurer's estimate of ultimate losses over a single accounting year. In the distribution-free chain-ladder framework of [[Thomas Mack]], they derived analytic expressions for the one-year prediction error and connected the resulting quantity to solvency measurement.<ref name="cdr2008" /> The distinction between an ''ultimate'' reserving horizon and a ''one-year'' horizon became important under modern risk-based regulatory regimes. Subsequent Casualty Actuarial Society publications described the Merz–Wüthrich modification of the Mack model as a foundational approach to one-year reserve variability.<ref name="cas-one-year" /><ref>{{cite web|title=The Actuary and Enterprise Risk Management: Integrating Reserve Variability|url=https://www.casact.org/sites/default/files/2024-02/cas-monograph-no-12.pdf|publisher=Casualty Actuarial Society|year=2024|access-date=26 September 2026}}</ref> His reserving research has also treated dependence between run-off triangles, the Bornhuetter–Ferguson method, paid-incurred chain models and Tweedie compound-Poisson models.<ref>{{cite journal|last1=Alai|first1=Daniel H.|last2=Merz|first2=Michael|last3=Wüthrich|first3=Mario V.|title=Mean square error of prediction in the Bornhuetter–Ferguson claims reserving method|journal=Annals of Actuarial Science|volume=5|issue=1|pages=7–31|year=2011|doi=10.1017/S1748499510000026}}</ref><ref>{{cite journal|last1=Merz|first1=Michael|last2=Wüthrich|first2=Mario V.|last3=Hashorva|first3=Enkelejd|title=Dependence modelling in multivariate claims run-off triangles|journal=Annals of Actuarial Science|volume=7|issue=1|pages=3–25|year=2013|doi=10.1017/S1748499512000127}}</ref> === Valuation and solvency === A second long-running theme is the valuation of insurance liabilities in a way that is consistent with traded financial assets. With Hans Bühlmann and Hansjörg Furrer, Wüthrich wrote the first two editions of ''Market-Consistent Actuarial Valuation'', published in 2008 and 2010; he authored the revised third edition in 2016.<ref>{{cite book|last1=Wüthrich|first1=Mario Valentin|last2=Bühlmann|first2=Hans|last3=Furrer|first3=Hansjörg|title=Market-Consistent Actuarial Valuation|edition=1st|series=EAA Series|publisher=Springer|year=2008|doi=10.1007/978-3-540-73643-1|isbn=978-3-540-73642-4}}</ref><ref name="springer-bio" /> The framework combines actuarial valuation with concepts from financial mathematics such as stochastic discounting, replicating portfolios and hedging. With Merz he also wrote ''Financial Modeling, Actuarial Valuation and Solvency in Insurance'' (2013), which develops a mathematical framework for solvency and asset-liability questions in incomplete markets.<ref>{{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Financial Modeling, Actuarial Valuation and Solvency in Insurance|series=Springer Finance|publisher=Springer|year=2013|doi=10.1007/978-3-642-31392-9|isbn=978-3-642-31391-2}}</ref> === Machine learning and actuarial data science === From the late 2010s, Wüthrich became one of the actuarial researchers working systematically on deep learning and machine-learning methods for insurance. His 2018 paper ''Neural networks applied to chain–ladder reserving'' used individual claim information to refine traditional aggregate chain-ladder reserving.<ref name="nn-chain" /> A related paper, ''Machine learning in individual claims reserving'', examined prediction directly at the level of individual claims rather than only through aggregated run-off triangles.<ref>{{cite journal|last=Wüthrich|first=Mario V.|title=Machine learning in individual claims reserving|journal=Scandinavian Actuarial Journal|volume=2018|issue=6|pages=465–480|year=2018|doi=10.1080/03461238.2018.1428681}}</ref> With Ronald Richman, Wüthrich applied neural networks to multi-population mortality forecasting by extending the classical [[Lee–Carter model]]. Their model used representation learning to learn shared and population-specific structures from mortality data.<ref>{{cite journal|last1=Richman|first1=Ronald|last2=Wüthrich|first2=Mario V.|title=A neural network extension of the Lee–Carter model to multiple populations|journal=Annals of Actuarial Science|volume=15|issue=2|pages=346–366|year=2021|doi=10.1017/S1748499519000071}}</ref> Richman and Wüthrich later proposed ''LocalGLMnet'', a neural-network architecture designed to combine the predictive flexibility of deep learning with an additive structure that can be interpreted in a manner similar to a [[generalized linear model]].<ref name="localglm" /> The model uses feature-dependent regression coefficients learned by a neural network, permitting variable selection and local interpretation of the fitted model. Their work has also explored methods for making machine-learning models conform more closely to actuarial modelling principles. With Salvatore Scognamiglio, they developed the ''credibility transformer'', which incorporates a credibility-weighting mechanism into a transformer architecture for tabular insurance data.<ref name="credibility">{{cite journal|last1=Richman|first1=Ronald|last2=Scognamiglio|first2=Salvatore|last3=Wüthrich|first3=Mario V.|title=The credibility transformer|journal=European Actuarial Journal|volume=15|pages=345–379|year=2025|doi=10.1007/s13385-025-00413-y}}</ref> The paper received the International Actuarial Association's JoCo Best Paper Award in 2025.<ref name="astin-prizes">{{cite web|title=ASTIN prizes|url=https://actuaries.org/sections/astin/astin-prizes/|publisher=International Actuarial Association|access-date=26 September 2026}}</ref> Wüthrich and Merz's open-access 2023 textbook ''Statistical Foundations of Actuarial Learning and its Applications'' integrates classical actuarial statistics with modern predictive modelling. Its subjects include generalized linear models, Bayesian methods, regularization, forecast evaluation, neural networks, recurrent and convolutional architectures, natural-language processing and model interpretation.<ref name="statfound">{{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Statistical Foundations of Actuarial Learning and its Applications|series=Springer Actuarial|publisher=Springer|location=Cham|year=2023|doi=10.1007/978-3-031-12409-9|isbn=978-3-031-12409-9|doi-access=free}}</ref> In 2025 he also became lead author of the collaborative lecture notes ''AI Tools for Actuaries'', a continuing open teaching project intended to provide data-science and artificial-intelligence material for actuarial education.<ref>{{cite web|last1=Wüthrich|first1=Mario V.|last2=Richman|first2=Ronald|last3=Avanzi|first3=Benjamin|last4=Lindholm|first4=Mathias|last5=Maggi|first5=Marco|last6=Mayer|first6=Michael|last7=Schelldorfer|first7=Jürg|last8=Scognamiglio|first8=Salvatore|title=AI Tools for Actuaries|url=https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5162304|publisher=Social Science Research Network|date=24 August 2026|doi=10.2139/ssrn.5162304|access-date=26 September 2026}}</ref> === Fairness and discrimination in insurance pricing === Wüthrich has also studied the relationship between statistical prediction and anti-discrimination constraints in insurance. With Mathias Lindholm, Ronald Richman and Andreas Tsanakas, he developed a mathematical formulation of ''discrimination-free insurance pricing'' that distinguishes direct use of protected characteristics from indirect discrimination arising when other variables act as proxies.<ref name="fairness">{{cite journal|last1=Lindholm|first1=Mathias|last2=Richman|first2=Ronald|last3=Tsanakas|first3=Andreas|last4=Wüthrich|first4=Mario V.|title=Discrimination-free insurance pricing|journal=ASTIN Bulletin|volume=52|issue=1|pages=55–89|year=2022|doi=10.1017/asb.2021.23|doi-access=free}}</ref> Their formulation can be applied to both traditional statistical models and machine-learning models. The work also highlights a practical tension: detecting and correcting indirect discrimination can require information about protected characteristics even when those variables cannot be used directly for pricing.<ref name="fairness" /> A later paper by the same group used multi-task neural networks to estimate discrimination-free prices.<ref>{{cite journal|last1=Lindholm|first1=Mathias|last2=Richman|first2=Ronald|last3=Tsanakas|first3=Andreas|last4=Wüthrich|first4=Mario V.|title=A multi-task network approach for calculating discrimination-free insurance prices|journal=European Actuarial Journal|volume=14|pages=329–369|year=2024|doi=10.1007/s13385-023-00367-z|doi-access=free}}</ref> == Teaching and professional service == At ETH Zurich, Wüthrich directs actuarial studies within RiskLab. His recent teaching has included ''Non-Life Insurance: Mathematics and Statistics'', ''Data Science for Actuaries'' and ''Economic and Market-Consistent Actuarial Valuation''.<ref name="eth-teaching" /><ref>{{cite web|title=Mario Valentin Wüthrich: Course units in Spring Semester 2026|url=https://www.vvz.ethz.ch/Vorlesungsverzeichnis/dozent.view?ansicht=2&dozide=10017668&lang=en&semkez=2026S|publisher=ETH Zurich|access-date=26 September 2026}}</ref> His lecture material is used both in university teaching and in actuarial professional education. He was a member of the board of the Swiss Association of Actuaries from 2006 to 2018 and served as an editor of the ''ASTIN Bulletin'' before becoming Editor-in-Chief in 2018.<ref name="about" /><ref name="astin-editor" /> He has also held visiting or honorary academic appointments, including Honorary Visiting Professor at [[City, University of London]] from 2011 to 2022, Honorary Professor at [[University College London]] from 2013 to 2019 and an adjunct professorship at the [[University of Bologna]] from 2014 to 2016.<ref name="statfound" /> == Recognition == Wüthrich has received a number of prizes for papers in actuarial science. In 2017 he and Josef Teichmann received the Bob Alting von Geusau Prize of the AFIR-ERM Section of the International Actuarial Association for ''Consistent yield curve prediction''.<ref>{{cite web|title=Josef Teichmann and Mario Wüthrich: Bob Alting von Geusau Prize|url=https://math.ethz.ch/news-and-events/news/d-math-news/2017/10/josef-teichmann-and-mario-wuethrich-bob-alting-von-geusau-prize.html|publisher=ETH Zurich|date=5 October 2017|access-date=26 September 2026}}</ref> His paper ''Neural networks applied to chain-ladder reserving'' received the Best Paper Award at the 2018 International Congress of Actuaries.<ref name="about" /> With Ronald Richman he received the [[Institute and Faculty of Actuaries]]' Geoffrey Heywood Prize in 2020 for their work on neural-network mortality forecasting and the Brian Hey Prize in 2021 for ''LocalGLMnet''.<ref>{{cite web|title=Geoffrey Heywood Prize|url=https://actuaries.org.uk/about-us/prizes-and-awards/best-paper-prizes/geoffrey-heywood-prize/|publisher=Institute and Faculty of Actuaries|access-date=26 September 2026}}</ref><ref>{{cite web|title=Brian Hey Prize|url=https://actuaries.org.uk/about-us/prizes-and-awards/best-paper-prizes/brian-hey-prize/|publisher=Institute and Faculty of Actuaries|access-date=26 September 2026}}</ref> In the same year Wüthrich, Łukasz Delong and Mathias Lindholm received the Gauss Prize of the German Society of Insurance and Financial Mathematics and the German Actuarial Association for work on Tweedie's compound-Poisson model.<ref name="about" /> In 2025, ''The credibility transformer'', written with Richman and Scognamiglio, received the International Actuarial Association's JoCo Best Paper Award.<ref name="astin-prizes" /> == Selected works == === Books === * {{cite book|last1=Wüthrich|first1=Mario Valentin|last2=Bühlmann|first2=Hans|last3=Furrer|first3=Hansjörg|title=Market-Consistent Actuarial Valuation|edition=1st|series=EAA Series|publisher=Springer|year=2008|isbn=978-3-540-73642-4|doi=10.1007/978-3-540-73643-1}} * {{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Stochastic Claims Reserving Methods in Insurance|series=Wiley Finance|publisher=John Wiley & Sons|year=2008|isbn=978-0-470-72346-3|doi=10.1002/9781119206262}} * {{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Financial Modeling, Actuarial Valuation and Solvency in Insurance|series=Springer Finance|publisher=Springer|year=2013|isbn=978-3-642-31391-2|doi=10.1007/978-3-642-31392-9}} * {{cite book|last1=Merz|first1=Michael|last2=Wüthrich|first2=Mario V.|title=Mathematik für Wirtschaftswissenschaftler|publisher=Vahlen|year=2013|isbn=978-3-8006-4482-7|language=de}} * {{cite book|last=Wüthrich|first=Mario V.|title=Market-Consistent Actuarial Valuation|edition=3rd|series=EAA Series|publisher=Springer|year=2016|isbn=978-3-319-46635-4|doi=10.1007/978-3-319-46636-1}} * {{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Statistical Foundations of Actuarial Learning and its Applications|series=Springer Actuarial|publisher=Springer|year=2023|isbn=978-3-031-12409-9|doi=10.1007/978-3-031-12409-9|doi-access=free}} === Selected articles === * {{cite journal|last=Wüthrich|first=Mario V.|title=Scaling identity for crossing Brownian motion in a Poissonian potential|journal=Probability Theory and Related Fields|volume=112|issue=3|pages=299–319|year=1998|doi=10.1007/s004400050192}} * {{cite journal|last1=Merz|first1=Michael|last2=Wüthrich|first2=Mario V.|title=Modelling the claims development result for solvency purposes|journal=Casualty Actuarial Society E-Forum|issue=Fall|pages=542–568|year=2008}} * {{cite journal|last=Wüthrich|first=Mario V.|title=Machine learning in individual claims reserving|journal=Scandinavian Actuarial Journal|volume=2018|issue=6|pages=465–480|year=2018|doi=10.1080/03461238.2018.1428681}} * {{cite journal|last=Wüthrich|first=Mario V.|title=Neural networks applied to chain–ladder reserving|journal=European Actuarial Journal|volume=8|issue=2|pages=407–436|year=2018|doi=10.1007/s13385-018-0184-4}} * <nowiki>{{cite journal |last1=Richman |first1=Ronald |last2=Wüthrich |first2=Mario V. |title=A neural network extension of the Lee–Carter model to multiple populations |journal=Annals of Actuarial Science |volume=15 |issue=2 |pages=346–366 |year=2021 |doi=10.1017/S174</nowiki> m9t6xwrsio8c901jtmfdtz2ul8nh6xy 232074 232073 2026-09-26T05:08:25Z Ryblow 142974 /* */ 232074 wikitext text/x-wiki == Early life and education == Wüthrich was born on 19 May 1969.<ref name="thesis">{{cite thesis|last=Wüthrich|first=Mario Valentin|title=Crossing Brownian motion in a soft Poissonian potential|type=Doctoral dissertation|publisher=ETH Zurich|year=1999|doi=10.3929/ethz-a-002049781}}</ref> He studied mathematics at ETH Zurich and received the degree of ''Diplom-Mathematiker'' before continuing to doctoral study there. His 1999 dissertation, ''Crossing Brownian motion in a soft Poissonian potential'', was written under the supervision of [[Alain-Sol Sznitman]], with [[Erwin Bolthausen]] as co-examiner.<ref name="thesis" /> His early research was in probability theory and the mathematical theory of random media. In a series of papers in the late 1990s, he studied the behaviour of [[Brownian motion]] in Poissonian potentials, including fluctuations, geodesics and scaling relations.<ref>{{cite journal|last=Wüthrich|first=Mario V.|title=Fluctuation results for Brownian motion in a Poissonian potential|journal=Annales de l'Institut Henri Poincaré, Probabilités et Statistiques|volume=34|issue=3|pages=279–308|year=1998}}</ref><ref name="scaling">{{cite journal|last=Wüthrich|first=Mario V.|title=Scaling identity for crossing Brownian motion in a Poissonian potential|journal=Probability Theory and Related Fields|volume=112|issue=3|pages=299–319|year=1998|doi=10.1007/s004400050192}}</ref> This work belongs to the study of random environments and directed or crossing paths, rather than to actuarial mathematics, which became the main focus of his later career. == Career == After his doctorate Wüthrich spent a period in academic research before moving into the insurance industry. From 2000 to 2005 he worked at Winterthur Insurance in Switzerland, where his responsibilities included non-life claims reserving and work connected with the development and implementation of the [[Swiss Solvency Test]].<ref name="springer-bio">{{cite book|last=Wüthrich|first=Mario V.|title=Market-Consistent Actuarial Valuation|edition=3rd|series=EAA Series|publisher=Springer|location=Cham|year=2016|doi=10.1007/978-3-319-46636-1|isbn=978-3-319-46635-4}}</ref> He qualified as an Actuary SAA of the Swiss Association of Actuaries in 2004.<ref name="about">{{cite web|title=About|url=https://people.math.ethz.ch/~wueth/about.html|website=Mario Wüthrich, RiskLab, ETH Zurich|access-date=26 September 2026}}</ref> He returned to ETH Zurich in 2005, where he subsequently taught actuarial and financial mathematics and became Director of Actuarial Studies at RiskLab.<ref name="about" /><ref name="risklab-members">{{cite web|title=Members of RiskLab|url=https://risklab.ethz.ch/people/members.html|publisher=RiskLab Switzerland, ETH Zurich|access-date=26 September 2026}}</ref> ETH currently lists him as a ''Titularprofessor'' (adjunct professor) in the Department of Mathematics.<ref name="eth-current">{{cite web|title=Mario Wüthrich|url=https://math.ethz.ch/research/insurance-mathematics-stochastic-finance/mario-wuethrich.html|publisher=Department of Mathematics, ETH Zurich|access-date=26 September 2026}}</ref> His teaching has included courses in non-life insurance mathematics, actuarial data science and market-consistent actuarial valuation.<ref name="eth-teaching">{{cite web|title=Mario Valentin Wüthrich: Course units in Autumn Semester 2026|url=https://www.vvz.ethz.ch/Vorlesungsverzeichnis/dozent.view?ansicht=2&dozide=10017668&lang=en&semkez=2026W|publisher=ETH Zurich|access-date=26 September 2026}}</ref> Wüthrich served on the board of the Swiss Association of Actuaries from 2006 to 2018.<ref name="about" /> He joined the editorial team of the ''ASTIN Bulletin'' before succeeding Andrew Cairns as Editor-in-Chief in 2018.<ref name="astin-editor">{{cite journal|last=Wüthrich|first=Mario V.|title=Editorial|journal=ASTIN Bulletin|volume=48|issue=1|pages=1–2|year=2018|doi=10.1017/asb.2017.43}}</ref> The International Actuarial Association continues to list him in that position.<ref>{{cite web|title=ASTIN Bulletin|url=https://actuaries.org/publications/astin-bulletin/|publisher=International Actuarial Association|access-date=26 September 2026}}</ref> Since 2025 he has also been Senior Scientific Advisor to insureAI.<ref name="about" /> == Research == === Probability and random media === Wüthrich's doctoral and immediately pre-doctoral research was concerned with Brownian motion in random Poissonian media. His 1998 paper in ''Probability Theory and Related Fields'' established a scaling identity connecting fluctuation exponents for crossing Brownian motion in a Poissonian potential.<ref name="scaling" /> Other work from the same period treated fluctuation bounds, superdiffusive behaviour in two dimensions and geodesics in soft Poissonian potentials.<ref>{{cite journal|last=Wüthrich|first=Mario V.|title=Superdiffusive behavior of two-dimensional Brownian motion in a Poissonian potential|journal=The Annals of Probability|volume=26|issue=3|pages=1000–1015|year=1998}}</ref><ref>{{cite journal|last=Wüthrich|first=Mario V.|title=Geodesics and crossing Brownian motion in a soft Poissonian potential|journal=Annales de l'Institut Henri Poincaré, Probabilités et Statistiques|volume=35|issue=4|pages=509–529|year=1999}}</ref> After completing his doctorate, Wüthrich moved from academic research into the insurance industry. From 2000 to 2005 he worked at Winterthur Insurance, where his work focused on non-life claims reserving and solvency modelling. His later academic research at ETH Zurich developed these topics further, particularly in stochastic reserving, actuarial valuation and statistical modelling for insurance. === Claims reserving === A major strand of Wüthrich's research concerns stochastic modelling of outstanding claims in property and casualty insurance. His 2008 book with Michael Merz, ''Stochastic Claims Reserving Methods in Insurance'', develops stochastic versions of classical reserving techniques and methods for quantifying prediction uncertainty.<ref name="scrm">{{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Stochastic Claims Reserving Methods in Insurance|series=Wiley Finance|publisher=John Wiley & Sons|location=Chichester|year=2008|isbn=978-0-470-72346-3|doi=10.1002/9781119206262}}</ref> Merz and Wüthrich's work on the claims development result focused on the change in an insurer's estimate of ultimate losses over a single accounting year. In the distribution-free chain-ladder framework of [[Thomas Mack]], they derived analytic expressions for the one-year prediction error and connected the resulting quantity to solvency measurement.<ref name="cdr2008">{{cite journal|last1=Merz|first1=Michael|last2=Wüthrich|first2=Mario V.|title=Modelling the claims development result for solvency purposes|journal=Casualty Actuarial Society E-Forum|issue=Fall|pages=542–568|year=2008|url=https://www.casact.org/abstract/modeling-claims-development-result-solvency-purposes}}</ref> The distinction between an ''ultimate'' reserving horizon and a ''one-year'' horizon became important under modern risk-based regulatory regimes. Subsequent Casualty Actuarial Society publications described the Merz–Wüthrich modification of the Mack model as a foundational approach to one-year reserve variability.<ref name="cas-one-year">{{cite web|title=A Practical Way to Estimate One-year Reserve Risk|url=https://www.casact.org/sites/default/files/database/forum_12sumforum_completesummer12.pdf|publisher=Casualty Actuarial Society|year=2012|access-date=26 September 2026}}</ref><ref>{{cite web|title=The Actuary and Enterprise Risk Management: Integrating Reserve Variability|url=https://www.casact.org/sites/default/files/2024-02/cas-monograph-no-12.pdf|publisher=Casualty Actuarial Society|year=2024|access-date=26 September 2026}}</ref> His reserving research has also treated dependence between run-off triangles, the Bornhuetter–Ferguson method, paid-incurred chain models and Tweedie compound-Poisson models.<ref>{{cite journal|last1=Alai|first1=Daniel H.|last2=Merz|first2=Michael|last3=Wüthrich|first3=Mario V.|title=Mean square error of prediction in the Bornhuetter–Ferguson claims reserving method|journal=Annals of Actuarial Science|volume=5|issue=1|pages=7–31|year=2011|doi=10.1017/S1748499510000026}}</ref><ref>{{cite journal|last1=Merz|first1=Michael|last2=Wüthrich|first2=Mario V.|last3=Hashorva|first3=Enkelejd|title=Dependence modelling in multivariate claims run-off triangles|journal=Annals of Actuarial Science|volume=7|issue=1|pages=3–25|year=2013|doi=10.1017/S1748499512000127}}</ref> === Valuation and solvency === A second long-running theme is the valuation of insurance liabilities in a way that is consistent with traded financial assets. With Hans Bühlmann and Hansjörg Furrer, Wüthrich wrote the first two editions of ''Market-Consistent Actuarial Valuation'', published in 2008 and 2010; he authored the revised third edition in 2016.<ref>{{cite book|last1=Wüthrich|first1=Mario Valentin|last2=Bühlmann|first2=Hans|last3=Furrer|first3=Hansjörg|title=Market-Consistent Actuarial Valuation|edition=1st|series=EAA Series|publisher=Springer|year=2008|doi=10.1007/978-3-540-73643-1|isbn=978-3-540-73642-4}}</ref><ref name="springer-bio" /> The framework combines actuarial valuation with concepts from financial mathematics such as stochastic discounting, replicating portfolios and hedging. With Merz he also wrote ''Financial Modeling, Actuarial Valuation and Solvency in Insurance'' (2013), which develops a mathematical framework for solvency and asset-liability questions in incomplete markets.<ref>{{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Financial Modeling, Actuarial Valuation and Solvency in Insurance|series=Springer Finance|publisher=Springer|year=2013|doi=10.1007/978-3-642-31392-9|isbn=978-3-642-31391-2}}</ref> === Machine learning and actuarial data science === From the late 2010s, Wüthrich became one of the actuarial researchers working systematically on deep learning and machine-learning methods for insurance. His 2018 paper ''Neural networks applied to chain–ladder reserving'' used individual claim information to refine traditional aggregate chain-ladder reserving.<ref name="nn-chain">{{cite journal|last=Wüthrich|first=Mario V.|title=Neural networks applied to chain–ladder reserving|journal=European Actuarial Journal|volume=8|issue=2|pages=407–436|year=2018|doi=10.1007/s13385-018-0184-4}}</ref> A related paper, ''Machine learning in individual claims reserving'', examined prediction directly at the level of individual claims rather than only through aggregated run-off triangles.<ref>{{cite journal|last=Wüthrich|first=Mario V.|title=Machine learning in individual claims reserving|journal=Scandinavian Actuarial Journal|volume=2018|issue=6|pages=465–480|year=2018|doi=10.1080/03461238.2018.1428681}}</ref> With Ronald Richman, Wüthrich applied neural networks to multi-population mortality forecasting by extending the classical [[Lee–Carter model]]. Their model used representation learning to learn shared and population-specific structures from mortality data.<ref>{{cite journal|last1=Richman|first1=Ronald|last2=Wüthrich|first2=Mario V.|title=A neural network extension of the Lee–Carter model to multiple populations|journal=Annals of Actuarial Science|volume=15|issue=2|pages=346–366|year=2021|doi=10.1017/S1748499519000071}}</ref> Richman and Wüthrich later proposed ''LocalGLMnet'', a neural-network architecture designed to combine the predictive flexibility of deep learning with an additive structure that can be interpreted in a manner similar to a [[generalized linear model]].<ref name="localglm">{{cite journal|last1=Richman|first1=Ronald|last2=Wüthrich|first2=Mario V.|title=LocalGLMnet: interpretable deep learning for tabular data|journal=Scandinavian Actuarial Journal|volume=2023|issue=1|pages=71–95|year=2023|doi=10.1080/03461238.2022.2081816}}</ref> The model uses feature-dependent regression coefficients learned by a neural network, permitting variable selection and local interpretation of the fitted model. Their work has also explored methods for making machine-learning models conform more closely to actuarial modelling principles. With Salvatore Scognamiglio, they developed the ''credibility transformer'', which incorporates a credibility-weighting mechanism into a transformer architecture for tabular insurance data.<ref name="credibility">{{cite journal|last1=Richman|first1=Ronald|last2=Scognamiglio|first2=Salvatore|last3=Wüthrich|first3=Mario V.|title=The credibility transformer|journal=European Actuarial Journal|volume=15|pages=345–379|year=2025|doi=10.1007/s13385-025-00413-y}}</ref> The paper received the International Actuarial Association's JoCo Best Paper Award in 2025.<ref name="astin-prizes">{{cite web|title=ASTIN prizes|url=https://actuaries.org/sections/astin/astin-prizes/|publisher=International Actuarial Association|access-date=26 September 2026}}</ref> Wüthrich and Merz's open-access 2023 textbook ''Statistical Foundations of Actuarial Learning and its Applications'' integrates classical actuarial statistics with modern predictive modelling. Its subjects include generalized linear models, Bayesian methods, regularization, forecast evaluation, neural networks, recurrent and convolutional architectures, natural-language processing and model interpretation.<ref name="statfound">{{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Statistical Foundations of Actuarial Learning and its Applications|series=Springer Actuarial|publisher=Springer|location=Cham|year=2023|doi=10.1007/978-3-031-12409-9|isbn=978-3-031-12409-9|doi-access=free}}</ref> In 2025 he also became lead author of the collaborative lecture notes ''AI Tools for Actuaries'', a continuing open teaching project intended to provide data-science and artificial-intelligence material for actuarial education.<ref>{{cite web|last1=Wüthrich|first1=Mario V.|last2=Richman|first2=Ronald|last3=Avanzi|first3=Benjamin|last4=Lindholm|first4=Mathias|last5=Maggi|first5=Marco|last6=Mayer|first6=Michael|last7=Schelldorfer|first7=Jürg|last8=Scognamiglio|first8=Salvatore|title=AI Tools for Actuaries|url=https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5162304|publisher=Social Science Research Network|date=24 August 2026|doi=10.2139/ssrn.5162304|access-date=26 September 2026}}</ref> === Fairness and discrimination in insurance pricing === Wüthrich has also studied the relationship between statistical prediction and anti-discrimination constraints in insurance. With Mathias Lindholm, Ronald Richman and Andreas Tsanakas, he developed a mathematical formulation of ''discrimination-free insurance pricing'' that distinguishes direct use of protected characteristics from indirect discrimination arising when other variables act as proxies.<ref name="fairness">{{cite journal|last1=Lindholm|first1=Mathias|last2=Richman|first2=Ronald|last3=Tsanakas|first3=Andreas|last4=Wüthrich|first4=Mario V.|title=Discrimination-free insurance pricing|journal=ASTIN Bulletin|volume=52|issue=1|pages=55–89|year=2022|doi=10.1017/asb.2021.23|doi-access=free}}</ref> Their formulation can be applied to both traditional statistical models and machine-learning models. The work also highlights a practical tension: detecting and correcting indirect discrimination can require information about protected characteristics even when those variables cannot be used directly for pricing.<ref name="fairness" /> A later paper by the same group used multi-task neural networks to estimate discrimination-free prices.<ref>{{cite journal|last1=Lindholm|first1=Mathias|last2=Richman|first2=Ronald|last3=Tsanakas|first3=Andreas|last4=Wüthrich|first4=Mario V.|title=A multi-task network approach for calculating discrimination-free insurance prices|journal=European Actuarial Journal|volume=14|pages=329–369|year=2024|doi=10.1007/s13385-023-00367-z|doi-access=free}}</ref> == Teaching and professional service == At ETH Zurich, Wüthrich directs actuarial studies within RiskLab. His recent teaching has included ''Non-Life Insurance: Mathematics and Statistics'', ''Data Science for Actuaries'' and ''Economic and Market-Consistent Actuarial Valuation''.<ref name="eth-teaching" /><ref>{{cite web|title=Mario Valentin Wüthrich: Course units in Spring Semester 2026|url=https://www.vvz.ethz.ch/Vorlesungsverzeichnis/dozent.view?ansicht=2&dozide=10017668&lang=en&semkez=2026S|publisher=ETH Zurich|access-date=26 September 2026}}</ref> His lecture material is used both in university teaching and in actuarial professional education. He was a member of the board of the Swiss Association of Actuaries from 2006 to 2018 and served as an editor of the ''ASTIN Bulletin'' before becoming Editor-in-Chief in 2018.<ref name="about" /><ref name="astin-editor" /> He has also held visiting or honorary academic appointments, including Honorary Visiting Professor at [[City, University of London]] from 2011 to 2022, Honorary Professor at [[University College London]] from 2013 to 2019 and an adjunct professorship at the [[University of Bologna]] from 2014 to 2016.<ref name="statfound" /> == Recognition == Wüthrich has received a number of prizes for papers in actuarial science. In 2017 he and Josef Teichmann received the Bob Alting von Geusau Prize of the AFIR-ERM Section of the International Actuarial Association for ''Consistent yield curve prediction''.<ref>{{cite web|title=Josef Teichmann and Mario Wüthrich: Bob Alting von Geusau Prize|url=https://math.ethz.ch/news-and-events/news/d-math-news/2017/10/josef-teichmann-and-mario-wuethrich-bob-alting-von-geusau-prize.html|publisher=ETH Zurich|date=5 October 2017|access-date=26 September 2026}}</ref> His paper ''Neural networks applied to chain-ladder reserving'' received the Best Paper Award at the 2018 International Congress of Actuaries.<ref name="about" /> With Ronald Richman he received the [[Institute and Faculty of Actuaries]]' Geoffrey Heywood Prize in 2020 for their work on neural-network mortality forecasting and the Brian Hey Prize in 2021 for ''LocalGLMnet''.<ref>{{cite web|title=Geoffrey Heywood Prize|url=https://actuaries.org.uk/about-us/prizes-and-awards/best-paper-prizes/geoffrey-heywood-prize/|publisher=Institute and Faculty of Actuaries|access-date=26 September 2026}}</ref><ref>{{cite web|title=Brian Hey Prize|url=https://actuaries.org.uk/about-us/prizes-and-awards/best-paper-prizes/brian-hey-prize/|publisher=Institute and Faculty of Actuaries|access-date=26 September 2026}}</ref> In the same year Wüthrich, Łukasz Delong and Mathias Lindholm received the Gauss Prize of the German Society of Insurance and Financial Mathematics and the German Actuarial Association for work on Tweedie's compound-Poisson model.<ref name="about" /> In 2025, ''The credibility transformer'', written with Richman and Scognamiglio, received the International Actuarial Association's JoCo Best Paper Award.<ref name="astin-prizes" /> == Selected works == === Books === * {{cite book|last1=Wüthrich|first1=Mario Valentin|last2=Bühlmann|first2=Hans|last3=Furrer|first3=Hansjörg|title=Market-Consistent Actuarial Valuation|edition=1st|series=EAA Series|publisher=Springer|year=2008|isbn=978-3-540-73642-4|doi=10.1007/978-3-540-73643-1}} * {{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Stochastic Claims Reserving Methods in Insurance|series=Wiley Finance|publisher=John Wiley & Sons|year=2008|isbn=978-0-470-72346-3|doi=10.1002/9781119206262}} * {{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Financial Modeling, Actuarial Valuation and Solvency in Insurance|series=Springer Finance|publisher=Springer|year=2013|isbn=978-3-642-31391-2|doi=10.1007/978-3-642-31392-9}} * {{cite book|last1=Merz|first1=Michael|last2=Wüthrich|first2=Mario V.|title=Mathematik für Wirtschaftswissenschaftler|publisher=Vahlen|year=2013|isbn=978-3-8006-4482-7|language=de}} * {{cite book|last=Wüthrich|first=Mario V.|title=Market-Consistent Actuarial Valuation|edition=3rd|series=EAA Series|publisher=Springer|year=2016|isbn=978-3-319-46635-4|doi=10.1007/978-3-319-46636-1}} * {{cite book|last1=Wüthrich|first1=Mario V.|last2=Merz|first2=Michael|title=Statistical Foundations of Actuarial Learning and its Applications|series=Springer Actuarial|publisher=Springer|year=2023|isbn=978-3-031-12409-9|doi=10.1007/978-3-031-12409-9|doi-access=free}} === Selected articles === * {{cite journal|last=Wüthrich|first=Mario V.|title=Scaling identity for crossing Brownian motion in a Poissonian potential|journal=Probability Theory and Related Fields|volume=112|issue=3|pages=299–319|year=1998|doi=10.1007/s004400050192}} * {{cite journal|last1=Merz|first1=Michael|last2=Wüthrich|first2=Mario V.|title=Modelling the claims development result for solvency purposes|journal=Casualty Actuarial Society E-Forum|issue=Fall|pages=542–568|year=2008}} * {{cite journal|last=Wüthrich|first=Mario V.|title=Machine learning in individual claims reserving|journal=Scandinavian Actuarial Journal|volume=2018|issue=6|pages=465–480|year=2018|doi=10.1080/03461238.2018.1428681}} * {{cite journal|last=Wüthrich|first=Mario V.|title=Neural networks applied to chain–ladder reserving|journal=European Actuarial Journal|volume=8|issue=2|pages=407–436|year=2018|doi=10.1007/s13385-018-0184-4}} * <nowiki>{{cite journal |last1=Richman |first1=Ronald |last2=Wüthrich |first2=Mario V. |title=A neural network extension of the Lee–Carter model to multiple populations |journal=Annals of Actuarial Science |volume=15 |issue=2 |pages=346–366 |year=2021 |doi=10.1017/S174</nowiki> 91aru36njik0mvktv31roydgv3n87po