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In this paper, we obtain an optimal reinsurance contract explicitly in the form of excess-of-loss with a limit when the risk measure is Range-Value-at-Risk. Then we study optimal reinsurance with model uncertainty, where the uncertainty set contains a greatest element in the sense of stochastic order. Furthermore, we study the Stackelberg game in reinsurance with model uncertainty. In order to illustrate how our findings can be applied in practice to determine the optimal reinsurance contract, we perform an empirical study using the Wisconsin Local Government Property Insurance Fund dataset. Tweedie distributions are fit to the building and contents loss amounts from the property fund, and used to determine the optimal loading factor, and reinsurance contract corresponding to the loading factor. From the analysis, we discover that some policies have more recoveries from the optimal reinsurance contract than the premium paid, while others have smaller recoveries than the premium.

Optimal reinsurance with model uncertainty and Stackelberg game