Lundberg parameters for non standard risk processes

Abstract

We consider risk processes with delayed claims in a Markovian environment, and we study the asymptotic behaviour of finite and infinite horizon ruin probabilities under the small claim assumption. We also consider multivariate risk processes of the same kind, and we give upper and lower bounds for the Lundberg parameters of the corresponding total reserve. Our results have strong analogies with those one in the paper by Juri (Super modular order and Lundberg exponents, 2002).

Keywords:

• Shot noise process
• Markov modulated process
• Large deviations
• Lundberg parameter
• Supermodular order