A Study Of Insurance Risk Model With Investment

The ruin theory has always been the core problem in the modern insurance risk theories. In terms of ruin theory, those large claims are paid more attention for their giant damage brought to the insurance and this is why the scholars care more about them. With the rapid development of financial market and the fierce competition in the insurance, the classical risk model which only consider the profit of the premium cannot fulfill the the realistic management of the insurance company. In fact, the profit of investment has become an important part in the final profit of the insurance company. In this way, the researches of the risk model with investment have become the hot topic between the probability and statistics as well as the actuarial science. Besides, the researches about the ruin probability would give more practical guidance to the insurance.Different from the the researches about the classical model, the author launched an deep research about the two non-classical models:the risk model promoted by Li Zehui,et al (2005) which based on the insurance policy and the delayed-claims risk model supported from Waters (1985). The author constructed two models in which the insurance company is allowed to invest a constant fraction of its wealth in a stock market which is satisfied with the geometric Brownian motion and the remaining wealth in a bond with non negative interest force. In this surplus process in economic environment, the author studied the asymptotic behavior of ruin probabilities and the corresponding numerical simulation of the new models. The results had led a practical guidance to the insurance and also enriched the the theory of insurance.The contents of the paper are as follows:Chapter 1 is the introduction part which introduced the background of classical risk model, the heavy tailed distributions and the dependent structure. The various generalizations of the classical risk model and the relevant state of the research were paid more attention in this part.In chapter 2, the asymptotic behavior of ruin probabilities was investigated in a risk model based on the policy entrance process in which the insurance company is allowed to invest a constant fraction of its wealth in a stock market which is satisfied with the geometric Brownian motion and the remaining wealth in a bond with non negative interest force. In this model, the presence of pairwise quasi-asymptotically independent and dominant varying tailed claims, the expression of the wealth process were derived by the Ito formula and the finite-time, infinite ruin probabilities as well as corresponding numerical simulation were obtained.In chapter 3, the asymptotic behavior of ruin probabilities was investigated in a renewal risk model for delayed claims in which the insurance company is allowed to invest a constant fraction of its wealth in a stock market which is satisfied with the geometric Brownian motion and the remaining wealth in a bond with non negative interest force. Under the assumptions that the sequences of the main and delayed claims are negatively dependent and that the claim sizes belong to the heavy-tailed distribution class L?D, the expression of the wealth process was derived by the Ito formula, and the finite-time ruin probabilities were obtained.In Chapter 4, the author made a conclusion and provided an outlook for further study.