Robust optimal reinsurance contract with cooperation and competition
This paper investigates an optimal reinsurance contract formulation problem under the competition between n cooperative insurers and one reinsurer.The reinsurance contract consists of claim risk sharing strategy and reinsurance price.n insurers fully believe in their respective surplus process,while the reinsurer believes that each insurer's surplus process is un-certain.Each insurer's goal is to find an optimal claim risk sharing strategy so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth.The reinsurer's goal is to find an optimal reinsurance price so as to maximize the expected terminal wealth while minimizing the variance of the terminal wealth under the worst-case scenario of surplus process.Under the Stackelberg game framework,by using the stochastic control and stochastic dynamic programming techniques,we obtain the explicit solutions for the optimal claim risk sharing strat-egy and reinsurance price,furthermore derive the explicit solution for the optimal reinsurance contract.Finally,the influence of model parameter on the theoretical results is illustrated by numerical experiment,and some new reinsurance inspirations are obtained.
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