Stochastic Mortality Under Measure Changes

Biffis, Enrico; Denuit, Michel; Devolder, Pierre

doi:10.2139/ssrn.848267

Cited by 32 publications

(38 citation statements)

References 33 publications

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“…Milevsky & Promislow (2001), Dahl (2004), Miltersen & Persson (2005), Cairns, Blake & Dowd (2006), Bauer (2008), Barbarin (2008), Norberg (2010), Bauer, Benth & Kiesel (2012), Zhu & Bauer (2011), Zhu & Bauer (2012)). These are closely related to intensity models of mortality which were discussed by Biffis (2005), Biffis, Denuit & Devolder (2010), Hainaut & Devolder (2008), Luciano & Vigna (2008), and Schrager (2006), among others. Our main contribution is to provide a mathematically rigorous and transparent framework for this approach that generalizes and substantially clarifies previous contributions in the literature.…”

Section: Introductionsupporting

confidence: 53%

Stochastic mortality models: an infinite-dimensional approach

Tappe

Weber

2013

Finance Stoch

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Demographic projections of future mortality rates involve a high level of uncertainty and require stochastic mortality models. The current paper investigates forward mortality models driven by a (possibly infinite dimensional) Wiener process and a compensated Poisson random measure. A major innovation of the paper is the introduction of a family of processes called forward mortality improvements which provide a flexible tool for a simple construction of stochastic forward mortality models. In practice, the notion of mortality improvements are a convenient device for the quantification of changes in mortality rates over time that enables, for example, the detection of cohort effects.We show that the forward mortality rates satisfy Heath-Jarrow-Morton-type consistency conditions which translate to the forward mortality improvements. While the consistency conditions of the forward mortality rates are analogous to the classical conditions in the context of bond markets, the conditions of the forward mortality improvements possess a different structure: forward mortality models include a cohort parameter besides the time horizon; these two dimensions are coupled in the dynamics of consistent models of forwards mortality improvements. In order to obtain a unified framework, we transform the systems of Itô-processes which describe the forward mortality rates and improvements: in contrast to term-structure models, the corresponding stochastic partial differential equations (SPDEs) describe the random dynamics of two-dimensional surfaces rather than curves.

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Section: Introductionsupporting

confidence: 53%

Stochastic mortality models: an infinite-dimensional approach

Tappe

Weber

2013

Finance Stoch

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“…Among all stochastic mortality models, the Lee‐Carter (LC) model, proposed in 1992, is one of the most popular choices because of its ease of implementation and acceptable prediction errors in empirical studies. Various modifications of the LC model have been extended by Brouhns, Denuit, and Vermunt (), Renshaw and Haberman (), Cairns, Blake, and Dowd (), Li and Chan (), Biffis, Denuit, and Devolder (), and Hainaut () to attain a broader interpretation. Cairns, Blake, and Dowd () propose a two‐factor stochastic mortality model, the CBD model, in which a first factor affects mortality at all ages, whereas a second factor affects mortality at older ages much more than at younger ages.…”

Section: Introductionmentioning

confidence: 99%

“…Consequently, instead of using a Poisson model with a deterministic intensity function, an alternative means of fitting the number of deaths is to specify a doubly stochastic Poisson process, or Cox process (Cox, ), to capture the stochastic intensity. Biffis, Denuit, and Devolder () first implement a doubly stochastic setup in the LC model, introducing a class of equivalent probability measures for pricing life insurance liabilities and mortality‐indexed securities. Following the double stochastic setup proposed by Biffis, Denuit, and Devolder (), the second goal of this article is to provide an iterative fitting algorithm for estimating the Cox regression model in which mortality rates adhere to the RH model with non‐Gaussian innovations.…”

Section: Introductionmentioning

confidence: 99%

“…Biffis, Denuit, and Devolder () first implement a doubly stochastic setup in the LC model, introducing a class of equivalent probability measures for pricing life insurance liabilities and mortality‐indexed securities. Following the double stochastic setup proposed by Biffis, Denuit, and Devolder (), the second goal of this article is to provide an iterative fitting algorithm for estimating the Cox regression model in which mortality rates adhere to the RH model with non‐Gaussian innovations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mortality Modeling With Non‐Gaussian Innovations and Applications to the Valuation of Longevity Swaps

Wang¹,

Huang²,

Liu³

2013

J of Risk & Insurance

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This article provides an iterative fitting algorithm to generate maximum likelihood estimates under the Cox regression model and employs non-Gaussian distributions-the jump diffusion (JD), variance gamma (VG), and normal inverse Gaussian (NIG) distributions-to model the error terms of the Renshaw and Haberman (2006) (RH) model. In terms of mean absolute percentage error, the RH model with non-Gaussian innovations provides better mortality projections, using 1900-2009 mortality data from England and Wales, France, and Italy. Finally, the lower hedge costs of longevity swaps according to the RH model with non-Gaussian innovations are not only based on the lower swap curves implied by the best prediction model, but also in terms of the fatter tails of the unexpected losses it generates.Chou-Wen Wang is a Professor in the

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“…Other academic studies of mortality models include Booth et al (, ), Brouhns et al (), Brouhns et al (), Biffis (), Czado et al (), Koissi et al (), Renshaw and Haberman (), Delwarde et al (), Blake, Cairns, and Dowd (), Bauer et al (), Bauer, Benth, and Kiesel (), Hari et al (), Hunt and Blake (), Biffis, Denuit, and Devolder (), Debonneuil (), Cox et al (), Yang et al (), D'Amato et al (), Milidonis et al (), Wang, Huang, and Liu (), Zhu and Bauer (), Aleksic and Börger (), and Hainaut ().…”

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confidence: 99%

The New Life Market

Blake¹,

Cairns²,

Coughlan

et al. 2013

J of Risk & Insurance

110

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractThe huge economic significance of longevity risk for corporations, governments and individuals has begun to be recognized and quantified. By virtue of its size and prevalence, longevity risk is the most significant life-related risk exposure in financial terms and poses a potential threat to the whole system of retirement income provision. This paper reviews the birth and development of the Life Market, the market related to the transfer of longevity and mortality risks. We note that the emergence of a traded market in longevity-linked capital market instruments would act as a catalyst to help facilitate the development of annuity markets both in the developed and the developing world and protect the long-term viability of retirement income provision globally.

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Stochastic Mortality Under Measure Changes

Cited by 32 publications

References 33 publications

Stochastic mortality models: an infinite-dimensional approach

Stochastic mortality models: an infinite-dimensional approach

Mortality Modeling With Non‐Gaussian Innovations and Applications to the Valuation of Longevity Swaps

The New Life Market

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