Study Of The Compound Markov Binomial Model And Its Extended Model

In this thesis, we mainly study the compound Markov binomial model and the random premium income of the extended compound Markov binomial model. We consider the discount penalty function, the ultimate ruin probability, the distribution of surplus immediately before ruin, the distribution of the deficit at ruin, relativity's influence to risk model and Lundberg inequality.In chapter two, we study the compound Markov binomial risk model. The defective renewal equations for the conditional and unconditional Gerber-Shiu discount penalty function are obtained, and the formulas for the Gerber-Shiu discounted penalty function are gotten for u = 0. Moreover we derive the asymptotic estimate of the ultimate ruin probability, the distribution of surplus immediately before ruin, the distribution of the deficit at ruin, and obtain the formulas of these probabilities forw = 0. Finally, the Lundberg inequality is derived for the ruin probability.In chapter three, we consider the extended compound Markov binomial model which the arrival of insurance policies follow the binomial process. We get recursive formulas of the infinite survival probabilities and related factor's influence to the survival probability. A Lundberg upper bound for the ultimate ruin probability is obtained by the martingale approach.