Ruin Probabilities under a Markovian Risk Model

Abstract In this paper, a Markovian risk model is developed, in which the occurrence of the claims is described by a point process {N(t)} _t0 with N(t) being the number of jumps of a Markov chain during the interval 0, t]. For the model, the explicit form of the ruin probability (0) and the bound for the convergence rate of the ruin probability (u) are given by using the generalized renewal technique developed in this paper. Finally, we prove that the ruin probability (u) is a linear combination of some negative exponential functions in a special case when the claims are exponentially distributed and the Markov chain has an intensity matrix (q _ij ) _i,jE such that q _m = q _m1 and q _i = q _i(i+1), 1 i m–1.Supported by the National Natural Science Foundation of China (No. 19971072).