A Note on the Maximum Severity of Ruin and Related Problems

Abstract

Picard (1994) defines the maximum severity of ruin to be the largest deficit of a classical surplus process. Starting from initial surplus Mu, between the time of ruin and the time of recovery to surplus level 0. He gives a simple expression for the distribution function of Mu in terms of the probability of ultimate ruin. This paper first addresses the question of calculating the moments of Mu. It is not easy to achieve explicit expressions for these despite knowing the distribution function of Mu. We consider situations where explicit expressions can be obtained,as well as approximations. We also consider the closely related question of the maximum surplus prior to ruin