Research On Risk Model By Diffusion

This dissertation is devoted to the development of ruin theory in different risk models. We discuss two risk models by diffusion mainly. Firstly discuss continuous time model by diffusion which when the number of premium income is a Poisson process and multitype-insurance risk model. Introduce the concept of adjustment coefficient, discuss the character of surplus process, and get Lundberg inequality and formula of the ruin probability using two methods of traditional method and martingale. And get limit theory of renewal risk model by diffusion and the model when the number of premium income is a Poisson process by diffusion and multitype-insurance risk model by diffusion in renewal theory. And then discuss discrete time model of the compound binomial risk model by diffusion and the double binomial risk model by diffusion and the generalized compound binomial risk model by diffusion. Introduce the concept of adjustment coefficient, discuss the character of surplus process, and get Lundberg inequality and formula of the ruin probability using two methods of traditional method and martingale.