Reinsurance Strategy And Pricing Game Between Insurance And Reinsurance Company

With the development of the economy,the scale of insurance business continues expanding,and the competition in insurance market is becoming increasingly fierce.How to improve insurance companies' competitiveness and to reduce the risk of random claims by purchasing reinsurance is of great importance.Reinsurance,as an agreement based on original insurance contracts,is a transaction between insurance company and reinsurance company.It is also used by the insurance company to diversity risks,control potential claims and expand underwriting capacity.In the reinsurance market,the insurance company can decide whether to purchase reinsurance,while the reinsurance company can also decide whether to accept the reinsurance contract or not,there exist a game between them.Only the insurance company and the reinsurance both agree on it the contracts can be signed.We systematically analyze the best reinsurance strategy under the classical risk model and the diffusion risk model by assuming that both sides are to maximize the expected utility from terminal wealth.Firstly,we considered a reinsurance and pricing game problem between an insurance company and a reinsurance company for a diffusion risk model.Suppose that both the insure company and the reinsurance company take the increase of the expected terminal surplus utility as the condition of purchasing reinsurance and accepting reinsurance.By invoking the use of the dynamic programming principle,we obtain closed-form solutions of the reinsurance and pricing game under three cases for the insurer as well as the reinsurer with the exponential utility functions.As the result shows,the expected surplus utilities of the insurance company and the reinsurance company can increase under some conditions.When insurance companies are in the dominate stage,the optimal proportional reinsurance of insurance company is an increasing function of the insurance company risk aversion coefficient.It is negatively related to reinsurance price.When insurance company decides the proportion of reinsurance and the reinsurance company decide reinsurance premium,the optimal reinsurance premium of the reinsurance company is an increasing function of its risk aversion coefficient.If the reinsurance company dominate,the reinsurance company utility profit increases with the reinsurance premium.The insurance company utility profit increases at first and then decrease when reinsurance premium increases.Secondly,we consider a reinsurance and pricing game problem between an insure company and a reinsurance company with unequal status for a classical risk model.Suppose that the objectives of the insure company and the reinsurance company are to maximize the expected terminal surplus utility.The insure company and the reinsurance company both take the increase of the expected terminal surplus utility as the condition of purchasing reinsurance and accepting reinsurance.The insure company can decide whether to purchase proportional reinsurance according to the reinsurance price,while the reinsurance company can decide whether to accept the reinsurance contract.By invoking the use of the dynamic programming principle,we obtain closed-form conditions of the reinsurance and pricing game problems between the insure company and the reinsurance company under three cases for the insure company and the reinsurance company with an exponential utility function.The expected surplus utilities of the insurance company and the reinsurance company can increase under some conditions.We also obtain the analytical expressions of the reinsurance policy and the reinsurance price for expected value premium principle and exponential claim.Numerical examples are also provided to illustrate how the utility profit change when some model parameters vary.