Severity of ruin in a Markov-dependent risk model

We study the severity of ruin in a Markov-dependent risk model in which the claim interarrivals and claim amounts are influenced by an external Markov chain. A system of integro-differential equation of the severity of ruin, given the initial environment state, is derived. Explicit formulas for the severity of ruin are obtained when the initial surplus is zero or when all the claim amount distributions are from rational family. In the two state model, numerical illustration with exponential claim accounts are given.