School Seminars and Colloquia

Some explicit solutions for the joint density of the time of ruin and the deficit at ruin

Stochastic Processes Seminar

by David C M Dickson


Institution: Centre of Actuarial Studies, Department of Economics, The University of Melbourne
Date: Tue 27th May 2008
Time: 3:15 PM
Location: Room 103, Architecture, The University of Melbourne

Abstract: Using probabilistic arguments we obtain an integral expression for the
joint density of the time of ruin and the deficit at ruin. For the
classical risk model, we obtain the bivariate
Laplace transform of this joint density and invert it in the cases of
individual claims distributed as Erlang(2) and as a mixture of two
exponential distributions. As a consequence, we obtain
explicit solutions for the density of the time of ruin. We also
consider the situation of an Erlang(2) risk process.

For More Information: Contact: Prof Daniel Dufresne at dufresne@unimelb.edu.au or Dr Aihua Xia at xia@ms.unimelb.edu.au