Editors and Contributors

Editors-in-Chief

Jozef L. Teugels University Centre for Statistics, Katholieke Universiteit Leuven Belgium

Bjørn Sundt Vital Forsikring ASA Norway

Section Editors

Claims Distributions Gordon E. Willmot Department of Statistics and Actuarial Science, University of Waterloo Ontario, Canada

Collective Risk Theory Elias S.W. Shiu Statistics and Actuarial Sciences, University of Iowa USA

Direct Nonlife Insurance Gary G. Venter Guy Carpenter Instrat New York, USA

Greg Taylor Taylor Fry Consulting Actuaries Sydney, Australia

Economics Michel Denuit Institut des Sciences Actuarielles & Institut de Statistique, Universtite Catholique de Louvain Belgium

Marco Scarsini Dipartmiento di Statistica e Matematica Applicata, Universita di Torino Italy

Finance Andrew Cairns Actuarial Mathematics and Statistics, Heriot-Watt University Edinburgh, Scotland

Life, Pension and Health Insurance Angus S. Macdonald Actuarial Mathematics and Statistics, Heriot-Watt University Edinburgh, Scotland

Organizations, Journals and History Jean Lemaire Insurance and Risk Management Department, Wharton School, University of Pennsylvania Philadelphia, USA

Premium Calculation, Nonlife Shaun Wang SCOR Reinsurance Company, Itasca Illinois, USA Probability Theory Søren Asmussen Department of Theoretical Statistics, Aarhus University Denmark

Reinsurance Maria de Lourdes Centeno Instituto Superior de Economia e Gestao, Universidade Tecnica de Lisboa Portugal

Reserving Nonlife Richard Verrall Department of Actuarial Science and Statitics, City University London, UK

Statistics Josef G. Steinebach Mathematisches Institut, Universitaet zu Koeln Germany

Contributors Aase, Knut K. Norwegian School of Economics and Business Administration, Norway Ai, Jing The University of Texas at Austin, TX, USA Aitken, Amanda VWA, Australia Akselsen, Einar Gjensidige NOR Spareforsikring, Norway Albin, J.M.P. Chalmers University of Technology, Sweden Albrecher, Hansj¨org Graz University of Technology, Austria Albrecht, Peter University of Mannheim, Germany Andersen, Per Kragh University of Copenhagen, Denmark Ankney, Jonathan Deloitte & Touche, Chicago, IL, USA Asmussen, Søren Aarhus University, Denmark Aue, Alexander Universit¨at zu K¨oln, Germany Babcock, Nathan J. Conning Asset Management, Hartford, CT, USA Babu, Gutti Jogesh Pennsylvania State University, PA, USA Balakrishnan, N. McMaster University, Canada Barnett, Glen Insureware Pty Ltd, Australia Barto, Morris General Reinsurance Corporation, USA B¨auerle, Nicole University of Hannover, Germany Beall, Catherine Institute of Actuaries of Australia, Australia Beirlant, Jan Katholieke Universiteit Leuven, Belgium Bellis, Clare Macquarie University, Australia Benko, Maja Slovenian Association of Actuaries, Slovenia Bernet, Patrick M. Temple University, PA, USA Berthon, Jean Institut des Actuaires, France Bilikova, Maria Slovak Society of Actuaries, Slovakia Bing-Hong, Chen Cathay Life Insurance Company, Taiwan Bladt, Mogens IIMAS-UNAM, Mexico Blanchard, Ralph Travelers/Aetna, CT, USA Blanco, Robert Employers Reinsurance Corp, USA Bloom, Lauren M. American Academy of Actuaries, DC, USA Blum, Peter Converium Ltd and ETH Z¨urich, Switzerland Boa, J. Michael Casualty Actuarial Society, PA, USA Boller, Hans Peter Converium Ltd, Switzerland Bølviken, Erik University of Oslo, Norway Booth, Philip Cass Business School, City University, UK Borgan, Ørnulf University of Oslo, Norway Bosch Pr´ıncep, Manuela University of Barcelona, Spain Bowie, David Hymans Robertson, Glasgow, UK Boyer, M. Martin HEC Montr´eal, Universit´e de Montr´eal, Canada Boyer, Marcel Bell Canada and Universit´e de Montr´eal, Canada Brazauskas, Vytaras University of Wisconsin-Milwaukee, WI, USA Breedlove, William Society of Actuaries, IL, USA xiv Contributors Brender, Allan Office of the Superintendent of Financial Institutions, Canada Brockett, Patrick The University of Texas at Austin, TX, USA Brueckman, David C. Citizens Insurance Company, MI, USA Brusky, Ron CNA Insurance Europe, UK Buchanan, Robert Robert Buchanan Consulting Pty Ltd, Australia B¨uhlmann, Hans ETH Z¨urich, Switzerland Burnecki, Krzysztof Wrocław University of Technology, Poland Caeiro, Armando Instituto dos Actuarios Portugueses, Portugal Cai, Jun University of Waterloo, Canada Cairns, Andrew J.G. Heriot-Watt University, UK Camozzato, Leonardo MIBA, Brazil Carri`ere, J.F. Imperial College, UK, and University of Alberta, Canada Cassidy, Paul CGU Insurance, Australia Centeno, Maria de Lourdes CEMAPRE, ISEG, Technical University of Lisbon, Portugal Chambers, Morris W. London Life Insurance Company, USA Champion, R. La Trobe University, Australia Checa, M. Angeles Felipe KPMG and University of Barcelona, Spain Cheung, Ka Chun The University of Hong Kong, Hong Kong Citanna, Alessandro HEC and DELTA, France Claeskens, Gerda A&M University, TX, USA Coestier, B´en´edicte INRA-INAPG and UMR Economie Publique, France Cohen, Brett Tillinghast-Towers Perrin, Australia Conti, Benedetto Winterthur Group, Switzerland Courbage, Christophe The Geneva Association, Switzerland Crowder, Martin Imperial College of Science Technology and Medicine, UK Cummins, J. David University of Pennsylvania, PA, USA Cusick, Kelly Deloitte & Touche, Chicago, IL, USA Cuthbertson, Keith Imperial College of Science Technology and Medicine, UK Czapiewski, Colin Lane Clark & Peacock LLP, UK Da Silva, Carlos Manuel Pereira Instituto dos Actuarios Portugueses, Portugal Dacorogna, Michel Converium Ltd, Switzerland Dana, Rose-Anne Universite Paris Dauphine, France D’arcy, Stephen P. University of Illinois, IL, USA Davies, Peter New Zealand Society of Actuaries, New Zealand de Alba, Enrique Instituto Tecnol´ogico Aut´onomo de M´exico, Mexico D¸ebicki, Krzysztof University of Wrocław, Poland, and CWI, The Netherlands Denuit, Michel Katholieke Universiteit Leuven, Belgium Derrig, Richard A. Automobile Insurers Bureau of Massachusetts, MA, USA Dhaene, Jan Katholieke Universiteit Leuven, Belgium Di Lorenzo, Emilia University of Naples, Italy Dickson, David C.M. The University of Melbourne, Australia Dierckx, Goedele Katholieke Universiteit Leuven, Belgium Doney, R.A. University of Manchester, UK Dorrington, Robert University of Cape Town, South Africa Dowd, Kevin Nottingham University, UK Drekic, Steve University of Waterloo, Canada Duan, Jin-Chuan University of Toronto, Canada Dubin, Alan Zion Insurance Company Ltd., Israel Eben, Kryˇstof Czech Academy of Sciences, Czech Republic Eisen, Roland Goethe-Universit¨at, Germany Elsen, Gerda Association Royale des Actuaires Belges, Belgium Contributors xv Eriksen, Tor University of Karlstad (retired), Sweden Eyland, Arne Aktuarene, Norway Falk, Erik Benefit Network, Norway Feldblum, Sholom Liberty Mutual, MA, USA Fellingham, Gilbert W. Brigham Young University, UT, USA Ferrara, Giovanna Actuary Roma, Italy Finger, Robert J. Irvine, CA, USA Fombaron, Nathalie Universite Paris X-Nanterre, France Forfar, David O. Heriot-Watt University, UK Forker, Arlene Tillinghast-Towers Perrin, Australia Franke, J¨urgen Universit¨at Kaiserslautern, Germany Frees, Edward W. University of Wisconsin-Madison, WI, USA Fry, Martin Taylor Fry Consulting Actuaries, Sydney, Australia Fulop, Andras University of Toronto, Canada Fuping, Zhou Tsinghua University, Beijing, People’s Republic of China Garrido, Jos´e Concordia University, Canada Gates, Paul Lane Clark & Peacock LLP, UK Gather, Ursula University of Dortmund, Germany Getzen, Thomas E. Temple University, PA, USA Gielens, Geert Katholieke Universiteit Leuven and Dexia, Belgium Glynn, Peter W. Stanford University, CA, USA Gollier, Christian University of Toulouse (IDEI and LEERNA), France Goovaerts, Marc J. Katholieke Universiteit Leuven, Belgium Grandell, Jan Royal Institute of Technology, Sweden Groll, Simon Abel IAA, Argentina Gr¨ ubel, Rudolf University of Hannover, Germany Gu´erard, Yves IAA, Canada Guillen, Montserrat University of Barcelona, Spain Guldberg, Alf FPK Konsult, Sweden Haegin, Thomas Converium Ltd, Switzerland Halliwell, Leigh J. American Re-Insurance Company, NJ, USA Han´ak, G´abor Hungarian Actuarial Society, Hungary Hand, David J. Imperial College of Science Technology and Medicine, UK Hang Chan, Ngai Chinese University of Hong Kong, Hong Kong, SAR H¨ardle, Wolfgang Humboldt-Universit¨at zu Berlin, Germany Hardy, Mary R. University of Waterloo, Canada Hart, Doreen British Actuarial Journal, UK Heerwagen, Finn DIP, Denmark Henderson, Vicky University of Oxford, UK Hesselager, Ole University of Copenhagen, Denmark Heyde, C.C. Australian National University, Australia and Columbia University, NY, USA Hickman, James University of Wisconsin-Madison, WI, USA Hjort, Nils Lid University of Oslo, Norway Hock, Chi Cheng Singapore Actuarial Society, Singapore Hoffman-Jørgensen, J. Aarhus University, Denmark Hojenberg, Sergio Instituto Actuarial Argentino, Argentina Højgaard, Bjarne Aalborg University, Denmark Holst, Lars Royal Institute of Technology, Sweden Hosford, Mary Fireman’s Fund Insurance Companies, MA, USA Hougaard, Philip H. Lundbeck A/S, Denmark Høyland, Tor Eivind Benefit Network, Norway Hoyt, Robert University of Georgia, GA, USA xvi Contributors Hubert, Mia Katholieke Universiteit Leuven, Belgium Hughes, David P. Standard Life (ASIA) Limited, Hong Kong, SAR Hurst, Christopher W. Allstate Insurance Company, IL, USA Iliffe, Amy E. American Society of Pension Actuaries, VA, USA Jacobsen, Martin University of Copenhagen, Denmark Jacobsson, Jarmo Federation of Accident Insurance Institutions, Finland Jaffe, Jay IACA, VA, USA Jean, Jaime Metlife M´exico, Mexico Jeleva, Meglena University of Nantes and EUREQua, France Jensen, Uwe Christian-Albrechts- Universit¨at, Germany Jewell†, William S. University of California at Berkeley, CA, USA Johnson, Paul Western World Insurance Group, NJ, USA Jones, Bruce L. University of Western Ontario, Canada Jones, Derek A. Milliman USA, NY, USA Kaas, Rob University of Amsterdam, The Netherlands Kamil, Hassan Persatuan Aktuari Malaysia, Malaysia Kampmann, Tim Deutsche Aktuar-Akademie GmbH, Germany Klein, Robert Georgia State University, GA, USA Klugman, Stuart A. Drake University, IA, USA Kl¨uppelberg, Claudia Munich University of Technology, Germany Koll, Tarmo Estonian Actuarial Society, Estonia Koutsopoulos, C.J. Hellenic Actuarial Society, Greece Kramer, Bert ORTEC, The Netherlands Krvavych, Yuri University of New South Wales, Australia K¨uhn, Christoph Johann Wolfgang Goethe-University, Germany Kupper, Josef ETH-Zentrum, Switzerland Kuriyama, Akira Asahi Mutual Life Insurance Co, Japan Lamens, Andr´e IAA, Belgium Lawless, J.F. University of Waterloo, Canada L’Ecuyer, Pierre Universit´e de Montr´eal, Canada Lemaire, Jean University of Pennsylvania, PA, USA Lenard, C.T. La Trobe University, Australia L´eveill´e, Ghislain Universit´e Laval, Canada Levine, George M. KPMG, CT, USA Lillevold, P°al University of Oslo, Norway Lin, X. Sheldon University of Toronto, Canada Lindgren, Georg Lund University, Sweden Low, C.W.F. Faculty of Actuaries, UK Luciani, Renee Cyprus Actuarial Association, Cyprus Lynch, James QBE Reinsurance, USA Macdonald, Angus S. Heriott-Watt University, Edinburgh, UK Machina, Mark J. University of California, CA, USA Mack, Thomas Non-Life, Munich Re Group, Germany MacNicol, Roger Jardine Lloyd Thompson, Glasgow, UK Malutov, Michail Northeastern University, Boston, MA, USA Mal´y, Marek National Institute of Public Health, Czech Republic Mandl, Petr Charles University, Czech Republic Martin-L¨of, Anders Stockholm University, Sweden Mata, Ana J. CNA Re, IL, USA McClenahan, Charles L. Mercer Risk, Finance & Insurance Consulting, IL, USA Meilijson, Isaac Tel Aviv University, Israel Melinsky, Eduardo Melinsky, Pellegrinelli y Asoc, Argentina Meyers, Glenn Insurance Services Office Inc, NJ, USA Contributors xvii Michaelson, Robin Formerly of Cass Business School, City University, UK Mildenhall, Stephen J. Aon Re Services, IL, USA Miller, Robert B. University of Wisconsin, WI, USA Mills, T.M. La Trobe University, Australia Mirzashvili, G. A.Razmadze Mathematical Institute, Georgia Møller, Thomas University of Copenhagen, Denmark Mormino, Carla Angela Istituto Italiano degli Attuari, Italy Morshed, Omer Sidat Hyder Morshed Associates (Pvt) Ltd, Pakistan Moultrie, Tom A. University of Cape Town, South Africa Muermann, Alexander University of Pennsylvania, PA, USA M¨ uller, Alfred Universit¨at Karlsruhe, Germany Natvig, Bent University of Oslo, Norway Neuhaus, Walther Gabler & Partners AS/Swiss Re, Norway Nitzsche, Dirk Imperial College of Science Technology and Medicine, UK Noncek, Matthew D. Conference of Consulting Actuaries, IL, USA Norberg, Ragnar London School of Economics and Political Science, UK Nyrhinen, Harri University of Helsinki, Finland O’Brien, Christopher David Nottingham University Business School, UK Oppong, Robert SSNIT, Ghana Orbanz, Ulrich Swiss Re Life and Health, Germany Ostaszewski, Krzysztof M. Illinois State University, IL, USA Ott, Martin Swiss Life Network, Switzerland Panjer, Harry H. University of Waterloo, Canada Papaioannou, Takis University of Piraeus, Greece Parameswaran, Siddharth QBE Insurance Ltd, Australia Patrik, Gary Swiss Reinsurance Americas Division (retired), USA Pawlitschko, J¨org University of Dortmund, Germany Pelsser, Antoon Erasmus University and Nationale-Nederlanden, The Netherlands Pentik¨ainen, Teivo CEO retired, Insurance Company Ilmarinen, Finland Perelman, Mario Instituto Actuarial Argentino, Argentina Perez Raffo, Rodolfo Instituto Actuarial Argentino, Argentina Pettere, Gaida Latvian Actuarial Association, Latvia Pflug, Georg University of Vienna, Austria Phillips, Tony Accident Fund Company, MI, USA Pistorius, Martijn R. Utrecht University, The Netherlands Pitacco, Ermanno University of Trieste, Italy Pitts, Susan M. University of Cambridge, UK Platen, Eckhard University of Technology, Australia Polanskyj, Peter Morgan Stanley & Co, NY, USA Pollard, John Macquarie University, Australia Priest, Colin Sigma Plus Consulting, Australia Prime‡, Catherine P&K Actuaries, Australia Racic-Zlibar, Tatjana Croatian Actuarial Association, Croatia Radtke, Michael University of Applied Sciences, Dortmund, Germany Ramsay, Colin M. University of Nebraska-Lincoln, NE, USA Rao, M. Bhaskara North Dakota State University, ND, and University of Cincinnati, OH, USA Richards, Stephen Prudential Insurance Company, UK Roberts, Gareth O. Lancaster University, UK Rolski, Tomasz Wrocław University, Poland xviii Contributors Romano, Sofia Colegio Nacional de Actuarios A.C., Mexico Rosenthal, Jeffrey S. University of Toronto, Canada Rousseeuw, Peter J. University of Antwerp, Belgium Rusaityte, Deimante University of Copenhagen, Denmark Ryd´en, Tobias Lund University, Sweden Rytgaard, Mette M. Danish Re, Denmark Salminen, Paavo ° Abo Akademi University, Finland Samorodnitsky, Gennady Cornell University, NY, USA Sandstr¨om, Arne F¨ors¨akringsf¨orbundet, Sweden Schmidli, Hanspeter University of Copenhagen, Denmark Schmidt, Klaus D. Technische Universit¨at Dresden, Germany Schmitter, Hans Swiss Reinsurance Company, Switzerland Seltmann, Astrid Central Union of Marine Underwriters Norway (CEFOR), Norway Shapiro, Arnold F. Penn State University, PA, USA Sherris, Michael University of New South Wales, Australia Shields, Meyer J.P. Morgan Securities, Inc, NY, USA Shiu, Elias S.W. University of Iowa, IA, USA Sibbett, Trevor Fleet, Hampshire, UK Sigman, Karl Columbia University, NY, USA Sonnenholzner, Michael University of Erlangen-Nuernberg, Germany Sørensen, Michael University of Copenhagen, Denmark Splitt, Andrea Swiss Re Germany, Germany Steele, J. Michael University of Pennsylvania, PA, USA Stramer, Osnat University of Iowa, IA, USA Stroi ´ nski, Krzysztof Polskie Stowarzyszenie Aktuariuszy, Poland Studer, H.J. Swiss Re, Switzerland Sundt, Bjørn Vital Forsikring ASA, Norway Szuch, William WSA Financial Consulting Pty Ltd, Australia Tapiero, Charles S. Groupe ESSEC, France Taylor, Greg Taylor Fry Consulting Actuaries, Australia Teixeira, Carlos Tillinghast-Towers Perrin, Brazil Tess, Daniel PricewaterhouseCoopers Actuarial, Australia Teugels, Jozef L. Katholieke Universiteit Leuven, Belgium Theodorou, John A. Technological Educational Institution of Epirus, Greece Thijssen, Jacco Tilburg University, The Netherlands Thorisson, Hermann University of Iceland, Iceland Tolley, H. Dennis Brigham Young University, UT, USA Tsai, Cary Chi-Liang National Taiwan University, Taiwan Tzovenis, Ioannis P. Technological Educational Institution of Epirus, Greece Underwood, Alice M. Casualty Actuarial Society, PA, USA Unwin, Antony University of Augsburg, Germany Van Aelst, Stefan Ghent University, Belgium Van Horebeek, Johan Centro de Investigaci´on en Matem´aticas, Mexico Van Vuure, Simon Amstelveen, The Netherlands Venter, Gary G. Guy Carpenter Instrat, NY, USA Veraverbeke, No¨el Limburgs Universitair Centrum, Belgium Vernic, Raluca University of Constanta, Romania Verrall, Richard City University, UK Vetzal, K.R. University of Waterloo, Canada Contributors xix Viswanathan, Krupa S. Temple University, PA, USA Vyncke, David Katholieke Universiteit Leuven, Belgium Wade, Roger KPMG LLP, TX, USA Wambach, Achim University of Erlangen-Nuernberg, Germany Ward, Kimberley A. American Assn of Ins Services, IL, USA Webber, Nick City University, UK Wegenkittl, Klaus Union Versicherungs-Aktiengesellschaft, Austria Weron, Rafał Wrocław University of Technology, Poland Wilkie, David InQA Limited, UK Wilkins, William R. Casualty Actuarial Society, PA, USA Willmot, Gordon E. University of Waterloo, Canada Witcraft, Susan Guy Carpenter & Co Inc, MN, USA Wolff, Ronald W. University of California, CA, USA Wolthuis, Henk University of Amsterdam, The Netherlands Wong, Johnny Prime Consulting China Ltd, Hong Kong, SAR Wynn, Henry P. Warwick University, UK Xekalaki, Evdokia Athens University of Economics and Business, Greece and Trinity College, Ireland Yang, Hailiang The University of Hong Kong, Hong Kong, SAR Young, Virginia R. University of Michigan, MI, USA Younis, Vicki Insurance Australia Group, Australia Zehnwirth, Ben Insureware, Australia Zhigljavsky, Anatoly Cardiff University, UK Zoricic, Dubravka Croatian Actuarial Association, Croatia Zweifel, Peter University of Zurich, Switzerland † William S. Jewell sadly passed away in January 2003. ‡ Catherine Prime sadly passed away in February 2004.