Risk Model Of Continuous-time Mixed Collection Of Premiums

In the classical risk model, premium income per every unit time remains the same. However, in the actual procedure of premium acquisition, premium income per unit time varies as an extraneous variable. In this thesis, firstly, we introduce both the random premium acquisition risk model and the random premium acquisition risk model with stochastic diffusion, and get the expression of ruin probability and Lundberg inequality of the risk model. Secondly, we promote the model, and consider the one-type, double-type and multi-type compound risk model that deals with premium acquired both at a constant rate and randomly. In the end, we could get Lundberg inequality satisfied by ultimate ruin probability and its general expression.In chapter 1, we introduce the risk theory as well as the classical risk model and the promotion of it.In chapter 2, we introduce the background elementary knowledge that will be used in this thesis.In chapter 3, firstly, we introduce premium acquisition homogeneouse double-poisson risk model. Secondly, we promote the model, and get double-poisson random premium acquisition risk model with stochastic diffusion. Then we will use martingale approach to discuss the ruin problem of these two types of risk models.In chapter 4, we promote the risk double-poisson models from chapter 3, and we get a risk model with a premium income acquired mixed—including both constant rate and randomly premium income. Then we will use martingale approach to discuss the ruin problem of these two types of risk models.In chapter 5, we introduce a continuous-time random premium acquisition multi-type-insurance compound risk model with stochastic diffusion and get the expression of ruin probability and Lundberg inequality.