School Seminars and Colloquia

The beta product distribution with complex parametersby

Stochastic Processes Seminar
Joint Seminar Series on Stochastic Processes and Financial Mathematics

by Daniel Dufresne

Institution: Centre for Actuarial Studies, Department of Economics, Uni of Melb
Date: Thu 15th November 2007
Time: 1:15 PM
Location: Room 213, Richard Berry Buiding, The University of Melbourne

Abstract: The talk will describe how the distribution of the product of two independent
beta variables, which has 2+2=4 parameters, actually extends to cases where some of those parameters are complex or negative. This has apparently not been noticed previously. An actuarial application is given:
in the classical risk theoretic model with Poisson claim arrivals,
consider the discounted value of claims nos. 3, 6,..., each claim having
an exponential distribution; it turns out that this discounted value has
the same distribution as the product of two independent variables, one a
complex-parameter beta product and the other a gamma. (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.)

For More Information: Prof Daniel Dufresne or Dr Aihua Xia