A Stackelberg reinsurance-investment game with derivatives trading

Abstract

This paper studies a stochastic Stackelberg differential reinsurance-investment game with derivatives trading under a stochastic volatility model. The reinsurer who occupies a monopoly position can price a reinsurance premium and invest her wealth in the financial market consisting of a riskless asset and a stock and derivatives tied to the stock. The insurer, the follower of the Stackelberg game, purchases proportional reinsurance from the reinsurer and invests in the same financial market. The main target of the reinsurer and the insurer is to seek their own optimal strategy to maximize the CARA utility of the relative performance. An explicit equilibrium strategy with derivatives trading is deduced by solving Hamilton-Jacobi-Bellman (HJB) equations sequentially. The equilibrium investment strategy demonstrates that the insurer and the reinsurer imitate each other’s investment strategies, showing a herd effect. In numerical experiments, the sensitivity of the equilibrium strategy to model parameters is analyzed. For the optimal investment strategy, we find that a short position in the derivative may switch to a long position with parameters changing, which provides investors with important decision-making information.