Ruin Probabilities under a MarkovianRisk Model

Abstract In this paper, a Markovian risk model is developed, inwhich the occurrence of the claims is described by a pointprocess {N(t)} _t0with N(t) being the number ofjumps of a Markov chain during the interval [0,t]. For the model, theexplicit form of the ruin probability (0) and the bound for theconvergence rate of the ruin probability (u) are given by using the generalizedrenewal technique developed in this paper. Finally, we provethat the ruin probability (u) is a linear combination of somenegative exponential functions in a special case when the claimsare exponentially distributed and the Markov chain has anintensity matrix (q _ij ) _i,jE such thatq _m = q _m1 andq _i = q _i(i+1), 1 i m–1.Supported by the National Natural Science Foundationof China (No. 19971072).