Optimal Investment and Combined Proportional-Excess of Loss Reinsurance with Stochastic Interest and Stochastic Volatility

For jump-diffusion risk model,we considered the problem of optimal investment and reinsurance.The insurance company can purchase reinsurance for claims and invest the surplus in a risk-free asset and a risky asset.We assume that the form of reinsurance is a combined proportional-excess of loss reinsurance.We also assume that the risk-free asset has stochastic interest and the risky asset has both stochastic interest and stochastic volatility.By solving the corresponding Hamilton-Jacobi-Bellman(HJB) equation,the closed-form expressions for the value function as well as the optimal investment and reinsurance policy were obtained.Especially,through an example we interpreted the results more specifically.