Robust Mean–Variance Hedging of Longevity Risk

Abstract

Parameter uncertainty and model misspecification can have a significant impact on the performance of hedging strategies for longevity risk. To mitigate this lack of robustness, we propose an approach in which the optimal hedge is determined by optimizing the worst‐case value of the objective function with respect to a set of plausible probability distributions. In the empirical analysis, we consider an insurer who hedges longevity risk using a longevity bond, and we compare the worst‐case (robust) optimal hedges with the classical optimal hedges in which parameter uncertainty and model misspecification are ignored. We find that unless the risk premium on the bond is close to zero, the robust optimal hedge is significantly less sensitive to variations in the underlying probability distribution. Moreover, the robust optimal hedge on average outperforms the nominal optimal hedge unless the probability distribution used by the nominal hedger is close to the true distribution.

Dynamic Hedging of Longevity Risk: The Effect of Trading Frequency

“…Despite the importance of longevity risk management, the existing studies focus mainly on static hedging strategies (Blake et al, 2006;Li and Hardy, 2011;Li and Luo, 2012;Cairns et al, 2014;Li et al, 2017). Although static hedging seems a reasonable choice when indemnity derivatives are used, it may be suboptimal for index-based derivatives.…”

Mortality/Longevity Risk-Minimization with or without Securitization

“…Thanks to [50], we deduce that m ≡ m 0 (constant process) if and only if τ is a pseudostopping time. This implies that U, defined in (22), is a null process. Therefore, we conclude that…”

“…While this mortality premium puzzle might exist, the 'poor and/or bad' specification of the model for the mortality plays an important role in getting those wrong prices for longevity bonds. In [22], they propose a robust mean-variance hedging approach to deal with parameter uncertainty and model misspecification.…”

“…To our knowledge, apart from the recent paper [23], all the existing literature about mortality and/or longevity assumes a specific model for mortality and derives the dynamics for longevity bond prices accordingly. For an up-to-date extensive list of relevant papers, see [22]. We follow the approach of [23].…”

Longevity risk and capital markets: the 2018–19 update

“…Dahl, 2004;Chen & Cox, 2009;Cowley & Cummins, 2005;Lin & Cox, 2005;Cairns et al, 2006a;Cox & Lin, 2007;Biffis & Blake, 2010;2013Wills & Sherris, 2010;Lane, 2011;Mazonas et al, 2011;Blake et al, 2013;Yang & Huang, 2013;Michaelson & Mulholland, 2014;MacMinn & Brockett, 2017;Bugler et al, 2020) • Management and hedging of longevity risk (e.g. Dahl & Møller, 2006;Friedberg & Webb, 2007;Cocco & Gomes, 2008;Tsai et al, 2010;Wang et al, 2010;Coughlan et al, 2011;Koijen et al, 2011;Li & Hardy, 2011;Tzeng et al, 2011;Wang et al, 2010;Ngai & Sherris, 2011;Barrieu et al, 2012;International Monetary Fund, 2012;Li & Luo, 2012;Cairns, 2013;Cox et al, 2013aCox et al, , 2013bQiao & Sherris, 2013;Cairns et al, 2014;Zelenko, 2014;Zhu & Bauer, 2014;Li et al, 2017a;Wong et al, 2017;D'Amato et al, 2018;Liu & Li, 2016…”