OPTIMAL CHANGE-LOSS REINSURANCE CONTRACT DESIGN UNDER TAIL RISK MEASURES FOR CATASTROPHE INSURANCE

. In this paper, the optimal reinsurance contract design problem for catastrophe insurance is studied using the general structure of reinsurance contracts, change-loss reinsurance. Closed-form solutions are derived under two tail risk measures, Value-at-Risk (VaR) and Conditional Tail Expectation (CTE). The results show that CTE is a robust risk measure in that the structure of the optimal reinsurance contract under CTE measure is always change-loss reinsurance. While the optimal reinsurance contract under VaR measure degenerates from change-loss reinsurance to quota-share reinsurance when the ceding company is less risk averse. The theoretical approach is also applied to earthquake insurance market in China's Yunnan Province, and explicit solutions to the optimal reinsurance contract design problem under both VaR and CTE measures are obtained in the paper.