Optimal Investment And Reinsurance Strategies Of Insurance Company

This paper studies the optimal investment and reinsurance strategies, using thestochastic theory, HJB equation, the optimal decision theory and other mathematical tools,from the view of risk in insurance. Based on the exponential distribution and gammadistribution, respectively, as the claims, we consider reinsurance、risk investment anddividend distribution and use dynamic model equation to rational distribution ofinvestment, reinsurance and other issues in order to maximize the expected dividendswhen bankruptcy.On the basis of the jump-diffusion risk model, when the claims is exponentialdistribution, the non-cheap proportional reinsurance and the assets can invest into non-riskassets and risk assets, and the earning will be paid once it reaches the standard fordividends, in order to maximize the expected dividends when bankruptcy, namely, get theoptimal value function. We get the equation for the optimal investment strategy and thevalue function by applying the HJB equation theory, then it will be applied to claims asexponential distribution, and finally we will get the explicit solution of optimal investmentstrategies which has practical significance. In numerical example, according to the effectof some parameters on the investment strategy, we can know that the investment strategyconforms to actual situation.On the basis of the jump-diffusion risk model, when the claims is gamma distribution,considered investment and dividend distribution, the assets can invest into non-risk assetsand risk assets, and the earning will be paid once it reaches the standard for dividends, inorder to maximize the expected dividends when bankruptcy, namely, get the optimal valuefunction. We get the equation for the optimal investment strategy and the value functionby applying the HJB equation theory, then it will be applied to claims as gammadistribution, and finally we will get the explicit solution of optimal investment strategieswhich has practical significance. In numerical example, according to the effect of someparameters on the investment strategy, we can know that the investment strategy conformsto actual situation.