Distributions Of The Ruin Probability For The Risk Process Perturbed By Diffusion

The risk model perturbed by diffusion is more practicable than the classical risk model. Research of risk model with perturbation is a difficulty of mathematics and actuarial science because it makes up of a compound Poisson process and a diffusion process.In this paper, the ruin probability of the risk model perturbed by diffusion is discussed, and some actuarial methods and risk control estimation that fit the disciplinarian of insurance development are proposed. At the same time , some practical problems for insurance estimation and risk control process are resolved, and a new method of risk forecast for all kinds of insurance institution is provided.The main results are summarized as follows:(1) With the character of risk model perturbed by diffusion, B-Q process is defined. Corresponding properties. based on (H. 0) process proposed by Hou Zhenting, is also presented.(2) Distributions of the ruin probability and distributions of the assets surplus before its ruin are discussed by B- Q process. That is to say, the most difficult open-problem of literature[18] is solved.(3) Concrete distributions are provided in the following models: the renewal risk model perturbed by diffusion , the compound Poisson risk model perturbed by diffusion, the double Poisson risk model perturbed by diffusion and the thinning Poisson risk model perturbed by diffusion. The limit theoremes about these models are proved.(4) Expectative results areobtained by stochastic simulation in the following models: the compound Poisson risk model perturbed by diffusion, the double Poisson risk model perturbed by diffusion and the thinning Poisson risk model perturbed by diffusion. The loca of continuous models and discrete models are presented and analysed.