On the severity of ruin in a Markov-modulated risk model

Abstract

We consider a Markov-modulated risk model in which the claim inter-arrivals, amounts and premiums are influenced by an external Markovian environment process. A system of Laplace transforms of the probabilities of the severity of ruin, given the initial environment state, is established from a system of integro-differential equations derived by Snoussi [The severity of ruin in Markov-modulated risk models Schweiz Aktuarver. Mitt., 2002, 1, 31–43]. In the two-state model, explicit formulas for probabilities of the severity of ruin are derived, when the initial reserve is zero or when both claim amount distributions are from the rational family. Numerical illustrations are also given.

Keywords:

• Markov-modulated risk model
• ruin probability
• severity of ruin
• external Markovian environment
• rational family of distributions

The author would like to thank Prof. José Garrido and an anonymous referee for their valuable comments and suggestions to improve the paper.

This research was funded by a CAS/SOA Ph.D. grant