Two Types Of Bankruptcy Problems The Cox Proportional Hazards Model

Risk theory is a hot topic in the present actuarial science and mathematics research. The main risk model we considered in the paper is the Cox model. In chapter 1, we briefly review the risk theory and its development.In chapter 2, we generalize the classical risk model and get double Cox risk model perturbed by diffusion. Then we get exponential upper bounds for the ruin probability by using martingale theory in this new model. Finally, the non-exponential upper bounds is obtained when c=0.In chapter 3, we construct a Multi-insurance Cox risk model and get the generalized Lundberg inequality for ruin probability. The upper bounds and the lower bounds for the adjustment coefficient and the explicit expression of the ruin probability are given when the occurrence of the claims have the same intensity process. We acquire the explicit expression for survival probability and the expectation of maximal aggregate loss and give the distribution of the supreme surplus before ruin. when the Multi-insurance Cox risk model predigest the Multi-insurance Poisson process.In chapter 4, we briefly summarize the whole paper and put forward the further tasks.