Ruin probabilities in models with a Markov chain dependence structure.

Summary In this paper we derive explicit expressions for the probability of ruin in a renewal risk model with dependence described-by/incorporated-in the real-valued random variable Zk = −cτk + Xk , namely the loss between the (k − 1)–th and the k–th claim. Here c represents the constant premium rate, τk the inter-arrival time between the (k − 1)–th and the k–th claim and Xk is the size of the k–th claim. The dependence structure among (Zk )k>0 is given/driven by a Markov chain with a transition kernel satisfying an ordinary differential equation with constant coefficients.