Mortality derivatives and the option to annuitise

Milevsky, Moshe A.; Promislow, S. David

doi:10.1016/s0167-6687(01)00093-2

Cited by 243 publications

(136 citation statements)

References 12 publications

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“…We model longevity risk following a well-established stream of literature (initiated by Milevsky and Promislow (2001)) and provide a continuous-time cohort-based description of mortality. The event of death of an individual is modelled through a Cox process, as the first jump time of a Poisson process with stochastic intensity.…”

Section: Longevity Riskmentioning

confidence: 99%

Assessing the Solvency of Insurance Portfolios Via a Continuous Time Cohort Model

Jevtic

Regis

2014

SSRN Journal

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This paper evaluates the solvency of a portfolio of assets and liabilities of an insurer subject to both longevity and financial risks. Liabilities are evaluated at fair-value and, as a consequence, interestrate risk can affect both the assets and the liabilities. Longevity risk is described via a continuous-time cohort model. We evaluate the effects of natural hedging strategies on the risk profile of an insurance portfolio in run-off. Numerical simulations, calibrated to UK historical data, show that systematic longevity risk is of particular importance and needs to be hedged. Natural hedging can improve the solvency of the insurer, if interest-rate risk is appropriately managed. We stress that asset allocation choices should not be independent of the composition of the liability portfolio of the insurer.

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Section: Longevity Riskmentioning

confidence: 99%

Assessing the Solvency of Insurance Portfolios Via a Continuous Time Cohort Model

Jevtic

Regis

2014

SSRN Journal

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“…11 As a consequence of this market incompleteness, arbitrage arguments are insufficient to obtain unique market prices of annuities and related products. This seriously complicates the fair valuation of liabilities depending on future survival 11 Sometimes, there are natural hedge possibilities, see, for example, Milevsky and Promislow (2001) or Cox and Lin (2007). See also Section 5.3. outcomes due to the presence of a (longevity) risk premium.…”

Section: On the Importance Of Longevity Riskmentioning

confidence: 99%

“…Sometimes, natural hedges exist, see, for example, Milevsky and Promislow (2001) or Cox and Lin (2007). We illustrate the diversification possibilities through product mix in Section 5.3.…”

Section: Longevity Risk Managementmentioning

confidence: 99%

Longevity Risk

2010

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SummaryMost of the western world has seen a steady increase in the average lifetime of its inhabitants over the past century. Although the past trends suggest that further changes in mortality rates are to be expected, considerable uncertainty exists regarding the future development of mortality. This type of uncertainty is referred to as longevity risk. This paper reviews the current state of the literature concerning longevity risk. First, we discuss the modeling of future mortality, including the Lee and Carter (J Am Stat Assoc 87:659-671, 1992)-approach, as well as other approaches. Second, we discuss the importance of longevity risk for the solvency of portfolios of pension and life insurance products. Finally, we investigate possibilities for longevity risk management. In particular, we consider longevity risk management through securitization and/or pension and insurance (re)design.

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“…2) a mean-reverting Brownian Makeham's law (Milevsky and Promislow, 2001). Note that Y t = σ t 0 e −m(t−s) dW λ s , which reduces to σW λ t when m = 0.…”

Section: Mortality Model and Financial Marketmentioning

confidence: 99%

“…Within the topic of stochastic mortality, recent papers by Milevsky and Promislow (2001), Dahl (2004), DiLoernzo and Sibillo (2003), and Cairns, Blake, and Dowd (2006) proposed specific models for the evolution of the hazard rate. Others, such as Blake and Burrows (2001), Biffis and Millossovich (2006), Boyle and Hardy (2004), Cox and Wang (2006), proposed and analyzed mortality-linked instruments.…”

Section: Introductionmentioning

confidence: 99%

Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities

Bayraktar

Milevsky

Promislow

et al. 2009

Journal of Economic Dynamics and Control

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We develop a theory for valuing non-diversifiable mortality risk in an incomplete market. We do this by assuming that the company issuing a mortality-contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of our paper is that the value of the life annuity is identical to the upper good deal bound of Cochrane and Saá-Requejo (2000) and of Björk and Slinko (2006) applied to our setting. A second result of our paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting value as an expectation with respect to an equivalent martingale measure (as in Blanchet-Scalliet, El Karoui, and Martellini (2005)), and from this representation, one can interpret the instantaneous Sharpe ratio as an annuity market's price of mortality risk.

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Mortality derivatives and the option to annuitise

Cited by 243 publications

References 12 publications

Assessing the Solvency of Insurance Portfolios Via a Continuous Time Cohort Model

Assessing the Solvency of Insurance Portfolios Via a Continuous Time Cohort Model

Longevity Risk

Valuation of mortality risk via the instantaneous Sharpe ratio: Applications to life annuities

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