The Research On The Risk Model With Two-sided Jumps

The risk model with two-sided jumps has been studied widely and got great development in recent years. In this paper, on the basis of risk model which considers current reserves and interest rate of compound Poisson risk model and markov modulated risk model, we combine the two-sided jumps risk model, obtain different risk models with related characteristics of bankruptcy and some conclusions. The main work is as follows:In chapter3, we consider current reserves and interest rate risk model with two-sided jumps. As we known, in the classical risk model, the claims process is composite Poisson process. But in the actual operations of some companies, the money that to invest may earn or compensate, therefore the gains could be positive or negative is more realistic. A system of integro-differential equations with boundary conditions satisfied by the moment-generating function, the nth moment of the discounted dividend payments prior to ruin and the discounted penalty function, are derived. Because the equation coefficient is various and complicated and it’s hard to find the display solution, so we use the Sinc meth-ods to derive an approximate solution; we also get the graphs of the discounted dividend payments and ruin probability.In chapter4, we discuss the dual risk model with two-sided jumps under the Markov regime-switching. We assume that the daily expend, the claim oc-currence and the claim amount are regulated by an external Markov chain. By computation, we obtain the integro-differential equations of the discounted div-idend payments prior to ruin in general case and in two-state situation; besides, explicit solutions to the integro-differential equations when the claim amounts follow exponential distribution are also derived.