A note on probability and severity of ruin for generalized Lindley claim size distribution

Abstract

It is well known that, in a classical continuous time surplus process with given insurer's initial surplus, closed-form expressions for the probability and severity of ruin (the probability that ruin occurs and that the insurer's deficit at the time of ruin is less than specified value), exist for few claim size distributions such as the exponential and mixed exponential distributions. This paper provides a closed-form expressions for the probability and severity of ruin in the case where the claim size follows the generalized Lindley distribution which contains as special cases the exponential and the Lindley distributions. An upper bound for the probability of ruin is obtained via Lundberg's inequality. Numerical applications are shown to illustrate the results.