Bounds for the ruin probability under a markovian modulated risk model

Abstract

In this paper, generalized bounds are developed for the ruin probability under a Markovian modulated risk model. First, lower and upper bounds in terms of NBU and NWU type distributions or functions are obtained which includes the exponential bound as a special case when the Cramer Condition is satisfied. The technique used here is a combination of the conjugation idea, the Markov renewal theorem and the induction method. Then, a numerical iteration method is proposed for obtaining tightened monotone bounds by using the developed lower and upper bounds. Finally, improved bounds are obtained in terms of the ladder height distribution and an example is used for illustration