Stackelberg Reinsurance Chain Under Model Ambiguity

In this paper, we consider a continuous-time version of a reinsurance chain, which is sequentially formed by $n+1$ companies, with the first company being the primary insurer and the rest being reinsurers. Because of possible model misspecification, all companies are ambiguous about the original risk of the primary insurer. We model each reinsurance contracting problem as a Stackelberg game, in which the assuming reinsurer acts as the leader while the ceding company is the follower. Reinsurance is priced using the mean-variance premium principle and all companies are risk neutral under their own beliefs. We obtain equilibrium indemnities, premium loadings, and distortions in closed form, all of which are proportional to the original risk, with the corresponding proportions decreasing along the chain. We also show that the reinsurance chain with ambiguity aversions in increasing order is optimal from the perspectives of both selfish individual companies and an unselfish central planner