The Research On Some Risk Models Under Absolute Ruin

In recent years, absolute ruin theory is becoming a popular topic of the risk theory. In this paper, we get some generalized risk models by extending the stochastic return on investments risk model and markovian environment risk model in some different aspects. And some results about the dividend and discounted penalty function are discussed. It mainly makes the following aspects of the research work:1. Based on the stochastic return on investments risk model with constan-t dividend barrier, we extend the constant dividend barrier to the threshold dividend strategy, in which the absolute ruin problem is also considered. We derive integro-differential equations for the expectation of the discounted pay-ments, the moment-generating function with certain boundary conditions. Fur-thermore, we obtain integro-differential equations for the Gerber-Shiu function. The approximate solutions of the present value of all dividend and Gerber-Shiu function is given by sine methods. Finally, we study the effect which caused by different aspects on the ruin probability when the claim size distribution is exponential.2. Under the markovian environment risk model with constant dividend barrier, we extend the constant dividend barrier to the threshold dividend strat-egy. In which the distribution of the claim amounts is driven by an underlying markov jump process. We also obtain Integro-differential equations with cer-tain boundary of the moment-generating function of the present value of all dividend,Gerber-Shiu function. Finally, we obtain approximate solutions of the present value of all dividend,Gerber-Shiu function by using sine methods.