Optimal reinsurance pricing, risk sharing and investment strategies in a joint reinsurer-insurer framework

We investigate the reinsurance contract and investment strategy problem between an insurer and a reinsurer under the continuous-time framework. For the reinsurance contract design, the joint interests of the insurer and the reinsurer are considered. That is, the insurer determines the claim risk sharing strategy, and the reinsurer determines the reinsurance price. The insurer and the reinsurer can invest in the common risk-free asset and different risky assets to increase their respective wealths. The competition between the insurer and the reinsurer is quantified through the relative performance. Both the insurer and the reinsurer aim at maximizing the expected value of the terminal pay-off while minimizing its variance. By using the stochastic optimal control technique, we derive analytically the optimal time-consistent investment strategy and obtain the optimal reinsurance contract. Finally, the influences of model parameters on the optimal reinsurance contract and time-consistent investment strategy are examined through numerical experiments.