The Research On Several Correlated Risk Models

In classical risk model and many extended risk models, the property of independence is an important assumption,but the assumption is a bit rigourous and falls short of the fact of insurance agents' management.Therefore, recently, many scholars have made some researches on the correlated risk models. This paper further investigates the correlated risk models in two aspects and works out the results surprisingly in accordance with that in classical risk model.In chapter 2, we get a new risk model through generalizing the risk model in reference literature[11]. It must meet these terms below: (1) The new risk model is composed of two risk models which are conditioned by diffusion;(2) In the separate two risk models, the distribution of the two types of claimed amount is conditioned by light-tails;(3) In the separate two risk models, the two types of claimed counting processes have some correlation. The new model is Where N₁(t)=N₁₁(t)+N₁₂(t), N₂(t)=N₂₂(t)+N₁₂(t), N₁₁(t), N₂₂(t),N₁₂(t)are three independent homogeneous Poisson processes. At first, we investigate into the adjustment coefficient and bankruptcy probability in the condition of independence;At second, we manage to translate the correlated case into the independent case in order to achieve the aim to investigate into the adjustment coefficient and bankruptcy probability in the condition of correlation.In chapter 3, we get a new risk model through generalizing the risk model in reference literature[12]. It must meet these terms below: (1)It is a continuous-time risk model conditioned by diffusion;(2)The distribution of the premium amount and the claimed amount is conditioned by diffusion; (3) The claimed counting process and the counting process who buy the insurance portfolios are generalized homogeneous Poisson processes.(4) The claimed number and the number who buy the insurance portfolios have some correlation. The new model isWhere {N₁(t);t≥0}, {N₂(t);t≥0}, {N₃(t);t≥0} are three independent generalized homogeneous Poisson processes. Firstly, we investigate into the adjustment coefficient and bankruptcy probability in the condition that the relation between the two types of counting processes is independent, Secondly, we manage to translate the correlated case into the independent case in order to achieve the aim to investigate into the adjustment coefficient and bankruptcy probability in the condition of correlation.