Reinsurance contracts under Stackelberg game and market equilibrium

In this paper, we investigate the robust reinsurance contracts under Stackelberg game and market equilibrium. Each reinsurance contract contains two decision makers, one insurer and one reinsurer. The insurer is ambiguity-neutral and adopts a loss-dependent premium principle to collect premium. The reinsurer is ambiguity-averse and is a Bayesian learner. By using the stochastic dynamic programming method and the inverse method, the analytical expressions of the optimal risk allocation proportion and reinsurance price are derived for the two types of reinsurance contracts. We shows that the loss-dependent premium principle has the penalty-reward nature. Both the reinsurance price and demand decrease as the extrapolative intensity increases. Learning has important significance and always puts down the reinsurance price and puts up the reinsurance demand. On the contrary, the reinsurer's ambiguity aversion raises the reinsurance price and decreases the reinsurance demand. Finally, numerical analysis reveals that the reinsurance price is greater under the Stackelberg game than that under the market equilibrium.