Research On Optimal Reinsurance And Investment Strategy Of Insurance Company

In recent years,the insurance industry has become a research hotspot in the financial sector.It is very difficult to satisfy insurance company's claims only by collecting premiums because of the market competition is fierce in insurance practice.In response to this problem,insurance companies generally take two approaches: on the one hand,insurance companies make risk investments on surpluses to gain profits from investments,which is in order to improve their ability to pay.On the other hand,insurance companies share some of their risks by taking the form of reinsurance.Therefore,the method that controlling asset investment,controlling reinsurance or controlling both them makes the results better,which has become a new research hotspot in risk theory.This paper takes the issue of optimal reinsurance and investment strategy of insurance companies as the research object and does the following work:strategy of insurance companies as the research object and does the following work:First of all,we did research on optimal investment and excess-of-loss reinsurance strategy with options.We mainly considered the question that insurance companies take European call option as investment object to carry out excess-of-loss reinsurance under the market conditions assumed by the Black-Scholes model.The main research method use the minimum ruin probability of the insurance company as the objective function and use the diffusion approximation method,the Hamilton-Jacobi-Bellman(HJB)equation to get explicit solutions of optimal investment and excess-of-loss reinsurance strategy including options.Next,we studied the optimal investment and hybrid reinsurance strategies under the Heston model.The form of reinsurance is mixed reinsurance,and mixed reinsurance is a combination of excess-of-loss reinsurance and proportional reinsurance.The insurance companies invest in two types,which are risk-free asset and risky asset whose price process satisfies the Heston's stochastic volatility model.This chapter presents two important conclusions by setting up the target function in the sense of maximizing the exponential utility and solving the HJB equation.One is proved that excess-of-loss reinsurance is superior to mixed reinsurance.The second is that getting strategies of the optimal investment and reinsurance,and obtaining the solution of the optimal value function,which is under pure excess loss reinsurance.And then,we studied the optimal investment and proportional reinsurance strategies for dependent multi-industry models.The insurance companies' process of claim uses the common shock dependent multi-type risk model,and insurance companies carry out the proportional reinsurance for each claim.The insurance companies invest in two types,which are risk-free market and risky market.Under the criterion of maximizing the mean-variance utility of the terminal wealth in this chapter,we change the original mean-variance problem into an auxiliary problem;we solve the auxiliary problem by linear quadratic(LQ)control theory and HJB equation.Deriving strategies of the optimal investment and proportional reinsurance,and obtaining the solution of the optimal value function.At last,we studied the optimal investment and excess-of-loss reinsurance strategies for dependent multi-industry models.The claims process of insurance companies uses the common shock dependent multi-type risk model,and insurance companies carry out the excess-of-loss reinsurance for each claim.The insurance companies invest in two types,which are risk-free market and risky market which used the CEV model.In this chapter,we set up the target function under maximizing the exponential utility of insurance company's terminal wealth,and getting the optimal investment of insurance companies,strategies of excess-of-loss reinsurance and the solution of the optimal value function by solving the HJB equation.