Black Box Optimization Framework for Reinsurance of Large Claims

Abstract: A framework for optimization of reinsurance strategy is proposed for an insurance company with several lines of business (LoB), maximizing the Economic Value of purchasing reinsurance. The economic value is defined as the sum of the average ceded loss, the deducted risk premium, and the reduction in the cost of capital. The framework relies on simulated large claims per LoB rather than specific distributions, which gives more degrees of freedom to the insurance company.  Three models are presented, two non non-linear optimization models and a benchmark model. One non-linear optimization model is on individual LoB level and the other one is on company level with additional constraints using space bounded black box algorithms. The benchmark model is a Brute Force method using quantile discretization of potential retention levels, that helps to visualize the optimization surface.  The best results are obtained by a two-stage optimization using a mixture of global and local optimization algorithms. The economic value is maximized by 30% and reinsurance premium is halved if the optimization is made at the company level, by putting more emphasis on reduction in the cost of capital and less to average ceded loss. The results indicate an over-fitting when using VaR as the risk measure, impacting reduction in the cost of capital. As an alternative, Average VaR is recommended being numerically more robust.