Parisian ruin probability for Markov additive risk processes

Abstract

Abstract In this paper, we consider a spectrally negative Markov additive risk process. Using the theory of Jordan chain, a compact formula of Parisian ruin probability is given. The formula depends only on the scale matrix of spectrally negative Markov additive risk processes and the transition rate matrix Λq $\Lambda^{q}$.

Keywords

• Markov additive risk process
• Parisian ruin
• Scale matrices