Lundberg-type Bounds for the Joint Distribution of Surplus Immediately Before and at Ruin under a Markov-modulated Risk Model

Andrew C.Y. Ng, Hailiang Yang
2005 ASTIN Bulletin: The Journal of the International Actuarial Association  
In this paper, we consider a Markov-modulated risk model (also called Markovian regime switching insurance risk model). Follow Asmussen (2000, 2003), by using the theory of Markov additive process, an exponential martingale is constructed and Lundberg-type upper bounds for the joint distribution of surplus immediately before and at ruin are obtained. As a natural corollary, bounds for the distribution of the deficit at ruin are obtained. We also present some numerical results to illustrate the tightness of the bound obtained in this paper.
doi:10.1017/s0515036100014288 fatcat:ftnwkqnpefakroloxycozpczai