Liability-Driven Investment in Longevity Risk Management
This paper studies optimal investment from the point of view of an investor with longevity-linked liabilities. The relevant optimization problems rarely are analytically tractable, but we are able to show numerically that liability driven investment can s
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Liability-Driven Investment in Longevity Risk Management Helena Aro and Teemu Pennanen
Abstract This paper studies optimal investment from the point of view of an investor with longevity-linked liabilities. The relevant optimization problems rarely are analytically tractable, but we are able to show numerically that liability driven investment can significantly outperform common strategies that do not take the liabilities into account. In problems without liabilities the advantage disappears, which suggests that the superiority of the proposed strategies is indeed based on connections between liabilities and asset returns. Keywords Longevity risk • Mortality risk • Stochastic mortality • Stochastic optimization • Hedging
5.1 Introduction Longevity risk, the uncertainty in future mortality developments, affects pension providers, life insurers, and governments. The population structure of developed countries is increasingly leaning towards the old, and the effects of medical advances and lifestyle choices on mortality remain unpredictable, which creates an increasingly acute need for life insurance and pension plans to hedge themselves against longevity risk. Various longevity-linked instruments have been proposed for the management of longevity risk; see e.g. [6, 7, 11, 21, 27]. It has been shown how such instruments, once in existence, can be used to hedge mortality risk exposures in pensions or life insurance liabilities [7, 12, 13, 15, 18, 26]. Indeed, demand for longevity-linked instruments appears to exist, and some longevity transactions have already taken place. However, a major challenge facing the development of longevity markets
H. Aro Finnish Financial Supervisory Authority, Helsinki, Finland e-mail: [email protected] T. Pennanen () Department of Mathematics, King’s College London, London, UK e-mail: [email protected] © Springer International Publishing Switzerland 2017 G. Consigli et al. (eds.), Optimal Financial Decision Making under Uncertainty, International Series in Operations Research & Management Science 245, DOI 10.1007/978-3-319-41613-7_5
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is the hedging of the risk that stems from issuing longevity-linked securities. The supply for mortality-linked instruments might increase if their cash-flows could be (partially) hedged by appropriately trading in assets for which liquid markets already exist. Such a development has been seen e.g. in options markets, which flourished after the publication of the seminal Black–Scholes–Merton model. Even though the cash flows of mortality-linked instruments cannot be perfectly replicated, it may be possible to diminish the residual risk by an appropriate choice of an investment strategy. This paper addresses the above issues by studying optimal investment from the point of view of an insurer with longevity-linked liabilities. As such problems are rarely analytically tractable, we employ a numerical procedure that adjusts the investment strategy according to the statistical properties of assets and liability as well
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