Efficient Hedging of Life Insurance Portfolio for Loss-Averse Insurers

This paper investigates the hedging of equity-linked life insurance portfolio for loss-averse insurers. We consider a general arbitrage-free financial market and an actuarial market composed of n-independent policyholders. As the combined market is incomplete, perfect hedging of any actuarial-financial payoff is not possible. Instead, we study the efficient hedging of n-size equity-linked life insurance portfolio for insurers who are only concerned with their losses. To this end, we consider stochastic control problems (under the real-world measure) in order to determine the optimal hedging strategies that either maximize the probability of successful hedge (called quantile hedging) or minimize the expectation for a class of shortfall loss functions (called shortfall hedging). We show that the optimal strategies depend both on actuarial and financial risks. Moreover, these strategies adapt not only to the size of the insurance portfolio but also to the risk-aversion of the insurer. Under the additional assumption of complete financial market, we derive the explicit forms of the optimal hedging strategies. The numerical results show that, for loss-averse insurers, the optimal strategies outperform the optimal mean-variance hedging strategy, demonstrating the relevance of adopting the optimal strategy according to the insurers' risk aversion and portfolio size.