A Risk Model Based on Markov Chains with Marked Transitions

Abstract

In this article, we introduce a multivariate risk process with multiple types of claims. This model is based on the so-called Markov chain with marked transitions introduced in He and Neuts.^{[ 13 ]} It allows dependencies among the claim frequencies, among the claim severities, as well as between claim frequencies and claim sizes. We first derive formulas for the probabilities ruin due to different types of losses using classical root-finding techniques and then we show that the ruin probabilities may be obtained by coupling the risk process to a fluid queue.

Keywords:

• Fluid models
• Markov chains with marked transitions
• Risk models
• Ruin probability

Mathematics Subject Classification:

• Primary 60J27
• Secondary 60G17

ACKNOWLEDGMENT

This research was funded by the National Sciences and Engineering Council of Canada.