The Study On Several Extended Discrete Time Risk Models

The rapid development of social economy has intensified competition of insurance market, in order to meet the needs of today’s insurance market, the classical insurance risk model is improved. And consider factors such as interest, investment in the risk model, it becomes a hot spot in the study of ruin theory. Therefore, we extend some risk models in this thesis, the model with variable interest rate and investment rate of return are studied, and the model of the random premium income is studied. The main work is as follows:1. We discuss a double-risk model of discrete time with variable interest rate. The distribution of the sustainable period of ruin and the distribution of surplus immediately when surplus turns back positive are obtained by the method of recursion. The time that the surplus process reach a given level x for the first time and the integral equation of ruin probability are derived.2. We study the compound Markov binomial model with random income. The defective renewed equation of the conditional and unconditional Gerber-Shiu penalty function are derived, and the asymptotic estimate of Gerber-Shiu discounted penalty function are obtained by the fundamental theorem of discrete renewed equation. Finally, we get the formula calculation of ruin probability and the surplus immediately before ruin by the penalty function.3. We consider a negative risk model in the negative binomial process with return on investment rates. The explicit expression of ruin probability and Lundberg inequality are obtained in the terms of some techniques from the martingale theory, and the explicit expression of conditional expectation of ruin time is given.