Optimal Risk Management with Reinsurance and its Counterparty Risk Hedging

Abstract

In this paper, we revisit the study of an optimal risk management strategy for an insurer who wants to maximize the expected utility by purchasing reinsurance and managing reinsurance counterparty risk with a default-free hedging instrument, where the reinsurance premium is calculated by the expected value principle and the price of the hedging instrument equals to the expected payoff plus a proportional loading. Different to previous studies, we exclude ex post moral hazard by imposing the no-sabotage condition on reinsurance contracts and derive the optimal strategy analytically. Surprisingly, we find that the stop-loss reinsurance is always optimal. The form of optimal hedging payoff, however, changes with different cost advantage between reinsurance and the hedging instrument. We further show that full risk transfer is optimal if and only if both reinsurance pricing and the hedging price are fair. Finally, numerical analyses are conducted to illustrate the effects of some interesting factors on the optimal risk management strategy.

Keywords: Counterparty risk, Hedging, Mossin's theorem, No-sabotage condition, Optimal reinsurance design