Special Double-insurance Type Risk Model Under Constant Interest Rate

In this paper,a special risk model is presented,which consider interest rate,premiums for a complex random process and might appearing twice claims.That's special double-insurance type risk model under constant interest rate. So the models in the existing references are promoted to more close to the reality.The main research contents and results in this text are as follows:Firstly,the ruin probability of a special double-insurance type risk model under constant interest rate is studied.At first the necessary condition of insurance com-pany's stably operation in this model is obtained;Then the existance of adjustment coefficient is proved.And two kinds of upper bounds of this model's ruin probability are obtained by structuring discrete martingale and using recursion method.Secondly,the live probability of a special double-insurance type risk model under constant interest rate is studied.We not only deduce the differential integral equation for live probability of this model in the infinite time, obtain the differential equation for live probability when premiums and claims are exponential distribution.But also we discuss the partial differential integral equation for live probability in the limited time.Thirdly,the live probability of a special double-insurance type risk model under constant interest rate with interference is studied.The differential integral equations ofψs(u) andψd(u) by using differential and Ito integral equation are obtained.So the differential integral equations ofψ(u) is obtained; The differential equations ofψs(u),ψd(u) andψ(u)are obtained when premiums and claims are exponential distribution .And the partial differential integral equation for live probability of this model in the limited time are studied.