Discounted Claims and Complex Parameter Beta Distributions Professor Daniel

Discounted Claims and Complex-Parameter Beta Distributions Professor Daniel Dufresne University of Melbourne 5 September 2008, 15:00-16:00 Salle/Room LB 921.04, J.W. McConnell (Library) Building SGW Campus, Concordia University Résumé/Abstract: In the classical risk theoretic model with Poisson claim arrivals and exponential claims, consider the discounted value of claims nos. 3, 6, 9, and so on. (To risk theory specialists, considering every third claim in a Poisson arrival process is the same as assuming waiting times are Erlang(3) in a Sparre-Andersen model.) The distribution of the discounted value of future claims will be found. It turns out that this is the same as the distribution of the product of two independent variables, one having a gamma distribution, the other a "complex-parameter beta product" distribution. The latter will be properly defined, it involves extending the usual beta distribution. ref: Beta Products with Complex Parameters", Research Paper No.164, Centre for Actuarial Studies University of Melbourne, 2007. http://www.economics.unimelb.edu.au/SITE/actwww/wps2007/No164.pdf Organisé par: Groupe ISM en mathématiques actuarielles et financières Organized by: ISM group in Actuarial and Financial Mathematics www.dms.umontreal.ca/~morales/seminar_main.htm