A closed-form approximation for deriving expected losses in excess loss life reinsurance

Abstract

Primary life insurers need to calculate life reinsurance recoverables for excess-of-loss life reinsurance treaties for solvency purposes as in Solvency II. However, assuming deterministic mortality, the recoverables of excess-of-loss treaties could be zero because the surviving lives are too few to trigger the excess-of-loss barrier. Resorting to simulation may be cumbersome as it may call for blending into a deterministic mortality model such as those of commercial vendors. In this paper we describe an alternative method to avoid simulation that is fast and accurate and can easily be blended into existing commercial software. The results can be used in many instances such as supervisory reporting, reinsurance pricing and risk management.

Keywords: Life reinsurance, excess loss treaties, Lyapunov central limit theorem