OPTIMAL TRADE CREDIT REINSURANCE PROGRAMS WITH SOLVENCY REQUIREMENTS

In this paper we study the design of the optimal strategy of reinsurance for a particular line of heavy-tailed non-life type of insurance, namely trade credit insurance. Optimality is achieved by maximizing sharehold-ers expected rate of return over a reisurance program composed of a proportional quota share treaty and a complex multi-layer excess-of-loss treaty with multiple reinstatements. The work participates to the debate on insurance firm risk management within the Solvency II framework by considering, in particular, the constraint imposed by the solvency capital requirement and by assuming, both for the insurer and the reinsurer, a pricing principle based on a cost-of-capital approach. Due to the nature of this type of insurance, we use a loss model that takes into account correlations between defaults. To cope with the complex payoff of the non-proportional treaty, the computation of the loss dis-tribution is performed within a Monte Carlo framework equipped with an additional importance sampling variance reduction technique. Finally, we discuss numerical results obtained for a realistic credit insurance portfolio