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,