Non Mean Reverting Affine Processes for Stochastic Mortality

Luciano, Elisa; Vigna, Elena

doi:10.2139/ssrn.724706

Cited by 73 publications

(71 citation statements)

References 59 publications

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“…The results obtained in Luciano and Vigna (2005) justify the choice, made in the present paper, of an a¢ ne, time-homogeneous intensity process, without mean reversion. In particular, we will use a non Gaussian Feller model, since in this case the intensity can never become negative.…”

Section: Selection Of the Intensitysupporting

confidence: 76%

“…The marginal Kaplan-Meier data are used also as inputs for the calibration of the analytical marginal survival functions, according to the methodology in Luciano and Vigna (2005).…”

Section: Description Of the Data Setmentioning

confidence: 99%

“…Their analytical expression is given by (20). The corresponding parameters are estimated by minimizing the mean square error between the Kaplan Meier and the analytical survival functions, similarly to Luciano and Vigna (2005). The estimated parameters are, respectively for males and females…”

Section: The Analytical Marginal Survival Functionsmentioning

confidence: 99%

“…The stochastic mortality approach has been proposed by Milevsky Luciano and Vigna (2005). The probabilistic setting however can be traced back to Brémaud (1981), and has been quite extensively applied in the …nancial literature on default arrival (see for instance the seminal works of Artzner and Delbaen (1992), Du¢ e and Singleton (1999) and Lando (1998)).…”

Section: Introductionmentioning

confidence: 99%

“…From Section 5 onwards we apply the theoretical framework and the calibration method to the data sample: we present the data set, …nd the empirical margins with the KaplanMeier methodology, apply the Wang and Wells'copula calibration and selection procedure, and compare its results with the ones of the omnibus or pseudo maximum likelihood procedure. We then derive the marginal survival functions, adapting the procedure in Luciano and Vigna (2005). In Section 6 the speci…c best …t copula obtained, together with the analytical margins, enables us to present an estimate of the joint survival function and to discuss the corresponding measures of time-dependent association, following the results in Spreeuw (2006).…”

Section: Introductionmentioning

confidence: 99%

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Modelling stochastic mortality for dependent lives

Luciano

Spreeuw

Vigna

2008

Insurance: Mathematics and Economics

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Stochastic mortality, i.e. modelling death arrival via a jump process with stochastic intensity, is gaining increasing reputation as a way to represent mortality risk. This paper represents a …rst attempt to model the mortality risk of couples of individuals, according to the stochastic intensity approach. We extend to couples the Cox processes set up, namely the idea that mortality is driven by a jump process whose intensity is itself a stochastic process, proper of a particular generation within each gender. Dependence between the survival times of the members of a couple is captured by an Archimedean copula. We also provide a methodology for …tting the joint survival function by working separately on the (analytical) copula and the (analytical) margins. First, we calibrate and select the best …t copula according to the methodology of Wang and Wells (2000b) for censored data. Then, we provide a sample-based calibration for the intensity, using a time-homogeneous, non mean-reverting, a¢ ne process: this gives the marginal survival functions. By coupling the best …t copula with the calibrated margins we obtain a joint survival function which incorporates the stochastic nature of mortality improvements. Several measures of time dependent association can be computed out of it.We apply the methodology to a well known insurance dataset, using a sample generation. The best …t copula turns out to be a Nelsen one, which implies not only positive dependency, but dependency increasing with age.JEL Classi…cation: G22

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Section: Selection Of the Intensitysupporting

confidence: 76%

“…The marginal Kaplan-Meier data are used also as inputs for the calibration of the analytical marginal survival functions, according to the methodology in Luciano and Vigna (2005).…”

Section: Description Of the Data Setmentioning

confidence: 99%

Section: The Analytical Marginal Survival Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Modelling stochastic mortality for dependent lives

Luciano

Spreeuw

Vigna

2008

Insurance: Mathematics and Economics

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Hedging longevity risk in defined contribution pension schemes

2023

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Pension schemes all over the world are under increasing pressure to efficiently hedge longevity risk imposed by ageing populations. In this work, we study an optimal investment problem for a defined contribution pension scheme that decides to hedge longevity risk using a mortality-linked security, typically a longevity bond. The pension scheme promises a minimum guarantee which allows the members to purchase lifetime annuities upon retirement. The scheme manager invests in the risky and riskless assets available on the market, including the longevity bond. We transform the corresponding constrained optimal investment problem into a single investment portfolio optimization problem by replicating future contributions from members and the minimum guarantee provided by the scheme. We solve the resulting optimization problem using the dynamic programming principle. Through a series of numerical studies, we show that the longevity risk has an important impact on the investment strategy performance. Our results add to the growing evidence supporting the use of mortality-linked securities for efficient hedging of longevity risk.

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Valuation of equity-indexed annuities with regime-switching jump diffusion risk and stochastic mortality risk

Qian

Wang

2012

Sci. China Math.

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Non Mean Reverting Affine Processes for Stochastic Mortality

Cited by 73 publications

References 59 publications

Modelling stochastic mortality for dependent lives

Modelling stochastic mortality for dependent lives

Hedging longevity risk in defined contribution pension schemes

Valuation of equity-indexed annuities with regime-switching jump diffusion risk and stochastic mortality risk

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