The Optimal Retrospective Reinsurance with the Minimum Risk-Adjusted Value

Retrospective premium is a premium rating plan that relies on the actual loss of the insurer during the policy period. It underwrites losses that have occurred in the past. The retrospective premium has been used in the reinsurance model in this paper. When the optimal criterion is to minimize the risk-adjusted value and the risk capital is measured by TVaR, the optimal ceded function under this model is in the form of stop-loss reinsurance. The minimum risk-adjusted value and the optimal retention have been obtained. Finally, through numerical simulation, we assumed that the loss has the exponential distribution, Pareto distribution and Gamma distribution, and explored the influence of the tax multiplier T and the parameter \rho on the optimal retention and the minimum risk adjusted-value. The results show that when other parameters are constant, as T increases, the optimal retention increases and the minimum risk-adjusted value decreases, and when other parameters are constant, the optimal retention and the minimum risk-adjusted value both increase with the increase of \rho.