The Research On Some Issues About Insurance Random Risk Model

Financial risk management has been advocated as the third major revolution during the history of finance, following the Markowitz portfolio theory and the Black-Scholes option pricing theory. In recent decades, we have witnessed explosive developments of this field. Ruin theory is the central part of risk theory that applies to insurance. Ruin probability is the most important index for measuring the solvency of insurance company, which can reflect the initial capital and premium, as well as the quantitative criterion of controlling risk. In recent years, the frequent natural disasters and the global financial crisis have brought a huge insurance claims, which ask the financial institutions and insurance companies for more profound understanding of risk management. With the development of insurance, financial risk management has important applications to insurance because every insurer makes investments. However, these has not been sufficiently emphasized by researchers in insurance mathematics.As a consequence, there is a critical need for modifications in which the evidences of heavy-tailedness and financial risks can be incorporated into evaluations. This dissertation aims to study the problems between the risk management and financial insurance from the perspective of the ruin probability. Based on the classical risk theory, this research takes the "big claim" as the main research object, combining with the modern actuarial theory, obtain a series of asymptotically equivalent for ruin probability in the delayed renewal risk model under the considering that the constant interest and the risk investment. We also use random simulation technology to simulate ruin probability and measure risk.The dissertation get the following conclusions:First, we obtain a series of asymptotic relationship for the ruin probabilities in the delayed renewal risk model under the assumption of constant interest with Pareto and D distributions of claim size. Second, we research the risk model under the situation of risk invest. Different methods are used to prove asymptotic equivalent with the same assumption. Besides, we analyze the relationship between fluctuation ratios and ruin probability. At last we adopt random simulate methods based on the theoretical models with the non-interest and interest rates of occasions. It is proved that ruin probability deceased when the growth of the initial surplus and interest force increases.