A Note on the Maximum Severity of Ruin and Related Problems

Picard (1994) defines the maximum severity of ruin, u , to be the largest deficit of a classical surplus process, starting from initial surplus u , between the time of ruin and the time of recovery to surplus level 0. He gives a simple expression for the distribution function of u M in terms of the probability of ultimate ruin. This paper first addresses the question of calculating the moments of u M . It is not easy to achieve explicit expressions for these despite knowing the distribution function of u M . 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. Keywords: ruin theory, classical risk model, maximum severity of ruin, maximum surplus prior to ruin