Risk Model With Two Types Of Claims

Risk theory, as a part of insurance-actuarial-mathematics, deals with stochastic models of an insurance and studies the probability of ruin. The classial risk model considers mainly one class of risk. But the insurance develops rapidily. The scale of the business expands increasly. Considering the limitations of the classial risk model with single-type-insurance, we construct a two-type-insurance risk models in this thesis. And the thesis studies risk model with two different classes of risk and whose relates aggregate claim process is the sum of two classes of claims.The thesis is divided into three sections according to contents:In Chapter 1, we mainly study ruin probability in risk model with two-type claims. We assume that the two claim number processes are independent Poisson and compound Poisson- Geometric processes respectively. At last we also estimateψ(u) and give a explicit forψ(0). The renewal equation has been studied, at the same time we prove thatψ(u,ω) satisfies the renewal equation:In Chapter 2, we mainly study ruin probability of a two-insurance risk processes in constant interest rate. The ruin probabilityψ_δ(u) is studied, we also get formula of the ruin probability and give a explicit expression forψ_δ(0).In Chapter 3, we mainly study a discrete insurance risk model, where the arrivals of claim follow negative binomial stochastic series and binomial stochastic series. The formulas of ultimate ruin probability and Lundberg inequality for this model are obtained.