Several Multi-line Model In Continuous Time Ruin Probability And Related Research

With continuous expanding of the risk operation's scale of insurance companies, the generalized risk model shows some limitations. Based on the existent conclusions, this thesis discusses several kinds of multitype-insurance risk models from different viewpoint.The first model is the multitype-insurance risk model with compound poisson process. In Chapter Three of the thesis, we generalize the classical risk model to the multitype-insurance models with compound poisson process. The study of the ruin probability is based on the study of an expected discounted penalty. First, we derive the integro-differential equation and the integro equation of the expected discounted penalty. Then we get the Laplace expression of it by using two different methods. Based on relationship between the ruin probability and the expected discounted penalty, we derive the Laplace expression of the ruin probability at last.The second model is multitype-insurance risk model with compound generalized homogeneous poisson process perturbed by diffusion. In Chapter Four of the thesis, we generalize the multitype-insurance risk model with compound poisson process to multitype-insurance risk model with compound generalized homogeneous poisson process, at the same time, we add an diffusion process to the model. First, The formulas of the ruin probability and Lundberg coefficient are obtained by the use of martingale. Second, we consider a decomposition of the ruin probability for the risk process perturbed by diffusion: caused by oscillation or by a claim. We derive the integro equations and integro-differential equations satisfied by them. And we also prove some properties of them. Finally, we present the explicit expression for these distributions when the claims are exponentially distributed.The third model is multitype-insurance risk model with interaction between classes of business. In Chapter Five of the thesis, we generalize Multitype-insurance risk model with compound poisson process to Multitype-insurance risk model with interaction between classes of business. We examine basic properties of the proposed risk process and study upper bounds for the ruin probability and the ruin probability itself by the use of martingale. We also compare the Lundberg exponents of independence model with the one of dependence model. At last, we derive the result that the dependence one is more dangerous.