| Ruin probability is an important scale and indicator, which provide a theoretical basis for people making the risk decision, to measure the degree and evaluate the size of insurance company risk. The classical Lundberg-Cramer risk model lay the foundation for bankruptcy theoretical research, but it has significant limitations in describing the actual operation of the insurance company. In recent years, many scholars modified the classical risk model from the premium income, interest rate, the claims process and claim size distribution and other aspects. How to create a more perfect risk model which is more in line with the actual operation of the insurance company is a popular topic researched by actuarial circle academic and insurance business scholar now.Reinsurance reduces the likelihood of an insurance company insolvency and improve the affordability of funds by diversifying and controlling risk, while the discrete time risk model can better simulate risk model of the insurance company. In this paper, we discuss the ruin probability for the discrete time insurance risk model with proportional reinsurance.The organizational structure of this article:Firstly, we introduces the origin and the main results of probability of bankruptcy, summarizes the extension model based on the classical theory as well. Secondly, we construct an Sparre Andersen risk model with interest force and proportional reinsurance enlightened by the classic Sparre Andersen risk model, we gain the e-R2 of the ruin probability upper boundary by martingale and the e-R2 of the ruin probability upper boundary by recursive techniques. Lastly, we consider ruin probabilities for discrete time process driven by proportional reinsurance and a strictly stationary interest rate process. The recursive integral equation of finite time ruin probability and the lower bound of infinite time ruin probability are given. Lundberg inequalities for the infinite ruin probabilities are derived given a stationary policy. |
PDF Full Text Request