Optimal Investment And Reinsurance Strategies For Insurance Companies And Reinsurers

The instability of the economic market and the growth of the incidence of human diseases have enhanced people's awareness of risk aversion and developed insurance industry.Choosing a suitable insurance company to purchase insurance has become a topic that people often talk about.As a profit-making institution,insurance companies need to make profits while providing risk protection to customers.However,it is not enough to merely collect premiums.Therefore,insurance companies need to adopt appropriate reinsurance and investment strategies to improve their ability to resist risks and make profits.For finding the best investment and reinsurance strategy,the main problem faced by insurance companies is how to maximize their expected utility wealth or minimize their bankruptcy probability.This paper focuses on the optimal management of a financial company that holds shares of both insurance companies and reinsurance companies.The financial company's goal is to maximize the index-expected utility function of the sum insurance companies and reinsurance companies terminal wealth-weighted.In order to closer the actual risk model,this paper assumes that the surplus process of insurance companies and reinsurance companies is characterized by the jump-diffusion process.Both insurance companies and reinsurance companies collect premiums according to the principle of expected premium value.In addition,insurance companies can not only manage risks by controlling the number of policies,but also disperse risks by proportional reinsurance.Both insurance companies and reinsurance companies invest in a risk-free asset and a risky asset,where risky assets here are described by geometric Brownian motion.This paper aims to maximize the exponential utility of terminal wealth.The optimal investment and reinsurance strategies are derived by using stochastic control theory and dynamic programming principle,martingale method and minimum and maximum martingale measure.The optimal strategies derived by these three methods are the same.