Ruin probabilities in models with a Markov chain dependence structure

Corina Constantinescu (1) , Dominik Kortschak (1) , Véronique Maume-Deschamps (2)

1 UNIL - Université de Lausanne = University of Lausanne
2 SAF - Laboratoire de Sciences Actuarielle et Financière

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.

Mots clés: Density satisfying ODE with constant coefficients; Ruin probability; Dependence; Markov chain; Random walk; Rational Laplace transform; Density satisfying ODE with constant coefficients.

Domaines: Probabilités [math.PR]

Corina Constantinescu, Dominik Kortschak, Véronique Maume-Deschamps. Ruin probabilities in models with a Markov chain dependence structure. Scandinavian Actuarial Journal, 2013, 6, pp.453-476. ⟨hal-00564804⟩