The Study Of Several Kinds Of Discrete Time Risk Models With Paying Dividends

With the development and intensifying competition of the insurance industry, the kinds of dividend insurance are more and more, and the study of risk model with dividend strategy is becoming a hot topic in the risk theoretical study. In this thesis, we build corresponding risk models with dividend strategy based on several discrete risk models, and mainly study the Gerber-Shiu discounted penalty function, the ruin probability, the duration of ruin, the distribution of the surplus prior to ruin, the distribution of deficit at ruin and other ruin variables of these models. The main content is following:1. On the basics of the compound Markov binomial model, we build a compound Markov binomial model with paying dividend. We get the defective renewed equation and the asymptotic estimate of the conditional and unconditional Gerber-Shiu discounted penalty function of this model, and the recursive formula and the asymptotic solution of the conditional and unconditional ruin probability, the conditional and unconditional distribution of the deficit at ruin and other ruin variables.2. We discuss double-type insurance compound binomial risk model with paying dividend, in which the dividend barrier is a general nonnegative integer. Discuss on the surplus more and less than dividend barrier, we get the defective renewed equation and the asymptotic expression of Gerber-Shiu discounted penalty function, the recursive formula of the ruin probability and the distribution of the deficit at ruin of this model under the two different conditions.3. We study a discrete risk model with special dividends strategy, and get the differential equation and analytical expression of the Gerber-Shiu discounted penalty function of this model. We get the analytical expression of the discounted penalty function, and also give the recursive formula of the distribution of the surplus prior to ruin and the ruin duration. besides, we give the numerical calculation example, and finally extend the model to a more general renewed risk model.