Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A M-TYPE RISK MODEL WITH MARKOV-MODULATED PREMIUM RATE

  • Yu, Wen-Guang (School of Statistics and Mathematics, Shandong Economic University)
  • Published : 2009.09.30
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Abstract

In this paper, we consider a m-type risk model with Markov-modulated premium rate. A integral equation for the conditional ruin probability is obtained. A recursive inequality for the ruin probability with the stationary initial distribution and the upper bound for the ruin probability with no initial reserve are given. A system of Laplace transforms of non-ruin probabilities, given the initial environment state, is established from a system of integro-differential equations. In the two-state model, explicit formulas for non-ruin probabilities are obtained when the initial reserve is zero or when both claim size distributions belong to the $K_n$-family, n $\in$ $N^+$ One example is given with claim sizes that have exponential distributions.

Keywords

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