Model The Uncertainty Of Optimal Investment And Reinsurance Strategy

In recent year, due to severe competition in the insurance industry, the insurance companies get a lot of benefits to improve their solvency from the investment of the money at its disposal. At the same time, in order to reduce the risk of large claims, the insurance company takes reinsurance policy for claims. Subject to the control of investment and reinsurance, maximizing the expected wealth utility and minimizing the probability of ruin have a great deal of theoretical and practical significance.Firstly, the paper studies the diffusion approximation of the classical risk model. The HJB equation of the minimal probability of ruin and the optimal stop-loss reinsurance is given. We obtain the explicit expression of the minimal probability of ruin and the optimal stop-loss reinsurance under the claim is exponential distribution and Erlang distribution. The effects of the parameters on the optimal retention level are obtained by numerical calculation. Secondly, we study the optimal investment and reinsurance in the jump-diffusion risk model under uncertainty. Under uncertainty of the surplus and investment, explicit expressions for the maximal expected exponential utility and the corresponding optimal policies are obtained.