Investigations to the optimal derivative-based investment and proportional reinsurance strategies

The optimal derivative-based investment and proportional reinsurance problems with stochastic volatility and jump risks are investigated. Assume that insurer possesses the constant absolute risk aversion preference. The insurer transfers part of insurance risk via purchasing proportional reinsurance and invests surplus in financial market with a risk-free bond, a risky stock described by the stochastic volatility jump diffusion model, and two non-redundant derivatives. The optimal strategies of reinsurance and investment with derivative trading are obtained in closed-form, while the optimal strategies with no derivative trading are numerically analyzed. The gain from derivative trading is analyzed by the method of certainty-equivalence. Our results illustrate that the value of derivative trading is always positive and sizeable, compared with the size of positions in the financial market. Moreover, under the assumption that the risks in the financial market are independent of those in the insurance market, the optimal strategy of reinsurance is independent of that of investment.