June 5, 2003:

Xiaowen Zhou (Concoria University)

"Ruin probabilities in perturbed risk models"

11:00 a.m. in N638 Ross

ABSTRACT:

In this talk we will first go over the classical risk model in actuarial mathematics. A well known result on the distribution of its ruin time, namely, the Seal's formula will be introduced. Then we will focus on the classical model perturbed by a Brownian motion (perturbed model). Using Ito's formula one can show that, in such a model, the ruin probability as a function of initial reserve and time is the unique solution of a certain partial-integral-differential equation. The Laplace transforms of ruin time can be derived from this equation. Perturbed models with exponential claims will be considered later in this talk. Those Laplace transforms can be inverted numerically in this special case. We will show how this can be carried out. Discussions and related plots will be given.