Optimal Reinsurance Under Var Criteria

In this paper, we mainly consider the optimal reinsurance under VaR risk measure. Let X be the loss to be incurred by an insurer. The insurer cedes part of the loss, say f(X), to a reinsurer, and thus the insurer retains a loss I_f(X)=X-f(X), where the function f(x) is called a ceded loss function and the function I_f(x)=x-f(x) a retained loss function. Meanwhile, the insurer pays a reinsurance premium, sayδ_f(x), to the reinsurer. Assuming f(x) is an increasing convex function, we derive the optimal reinsurance under the mean-variance premium principle. The results show that depending on the confidence level for VaR and the safety loading for the reinsurance premium, a change-loss reinsurance is optimal in some cases while a quota-share reinsurance is optimal in some other cases.This paper is organized as follows. In section 1, we introduce the development of reinsurance in China and some main results in reinsurance. In section 2, we establish the optimal reinsurance model and find out the optimal ceded loss function. Finally, in section 3, numerical simulations about three well-known risk distribution are presented. The results confirm the existence of the optimal reinsurance.