Optimal investment allocation in a Jump Diffusion Risk Model with bond and stock investments.
详细信息
文摘
This article pertains to the optimal asset allocation of surplus from an insurance company model. The insurance company is represented by a compound Poisson risk process which is perturbed by diffusion and has investments. The investments are in both risky and risk-free types of assets similar to stocks/real estate and bonds. The insurance company can borrow at a constant interest rate in the event of a negative surplus. Numerical simulations were done on the Pure Diffusion Model, Pure Diffusion Model with borrowing and the Jump Diffusion Risk Model. An exact solution to the Pure Diffusion Model was found and used to check the numerical accuracy of the simulations. Also, an inequality was found for the Pure Diffusion Model. The simulations showed an anomaly at certain interest rates. The Pure Diffusion Models were used to estimate the Jump Diffusion Risk Model with borrowing. Numerical analysis appeared to show that an optimal asset allocation range can be estimated for certain parameters and compared with insurance data. Using a conservative method to minimize the probability of ruin, a reasonable optimal asset allocation range for a typical insurance company was about 4.5 to 8.2 percent invested in risky stock/real estate assets. Additional simulations were performed to determine a potential relationship between the parameters that yielded "good" models. The results showed a relationship of 0.45 mu ＝ sigma2 between the stock drift and volatility parameters. Finally, the asymptotic form of the ruin probability was shown to be a power function.