Under The Stochastic Interest Rate Risk Model With Interference Of Bankruptcy

In the classical ruin theory, many risk problems in the perturbed compound Poissonrisk process have been studied widely. At the same time, a risk process with stochasticinterest rate is also a hot topic. In this paper we propose and study ruin problems inthe perturbed compound Poisson risk process under stochastic interest rate with jump.We get an integro-diferential equation with boundary conditions for ultimate ruin prob-ability firstly. Then we analyze the ruin probabilities respectively which are caused bya claim and an oscillation. The integro-diferential equations for these ruin probabilitiesand boundary conditions are derived. When claim sizes are exponentially distributed andno jumps in the stochastic interest force, the explicit diferential equations and boundaryconditions are derived. Based on the risk process under stochastic interest rate withoutjump formers studied, we generalize it to the perturbed compound Poisson risk processin the presence of stochastic interest rate with jump.The thesis is divided into four chapters according to contents:Chapter1is preface. Firstly we review the development and the generalization of theperturbed compound Poisson risk model and the risk model with stochastic interest rate,list some related probability knowledge, then we introduced the perturbed compoundPoisson risk process in the presence of stochastic interest rate with jump.In Chapter2, by using the technique of stochastic control, we find the integro-diferential equation for ultimate ruin probability and boundary conditions.In Chapter3, we continue analyzing the integro-diferential equations for ruin prob-abilities which are caused by a claim and an oscillation for the same model respectively.In Chapter4, we give the diferential equations for ruin probabilities under somespecific circumstances.