Estimating the joint survival probabilities of married individuals

Lisanne Sanders, Bertrand Melenberg

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We estimate the joint survival probability of spouses using a large random sample drawn from a Dutch census. As benchmarks we use two bivariate Weibull models. We consider more flexible models, using a semi-nonparametric approach, by extending the independent Weibull distribution using squared
polynomials. Also based on a nonparametric comparison, we find that extending the independent Weibull distribution by a squared third order polynomial shows the best performance. We illustrate our model by calculating remaining life expectancies and annuity values. We find that the husbands life expectancy at birth is generally increasing with his wifes age of death and the wifes life expectancy at birth is generally increasing with her husbands age of death. Ignoring the dependence between the remaining lifetimes of spouses may lead to an underestimation of the value of a joint annuity and an overestimation of the value of a single-life annuity, but less than suggested on the basis of the previous literature.
Original languageEnglish
Pages (from-to)88-106
JournalInsurance: Mathematics & Economics
Volume67
DOIs
Publication statusPublished - Mar 2016

Fingerprint

Life Expectancy
Survival Probability
Weibull Distribution
Weibull Model
Census
Lifetime
Benchmark
Polynomial
Model
Estimate
Life expectancy
Survival probability
Spouses
Life annuities
Weibull distribution

Keywords

  • Mortality
  • Life expectancy
  • Annuity
  • Non-parametrics
  • Joint survival

Cite this

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title = "Estimating the joint survival probabilities of married individuals",
abstract = "We estimate the joint survival probability of spouses using a large random sample drawn from a Dutch census. As benchmarks we use two bivariate Weibull models. We consider more flexible models, using a semi-nonparametric approach, by extending the independent Weibull distribution using squaredpolynomials. Also based on a nonparametric comparison, we find that extending the independent Weibull distribution by a squared third order polynomial shows the best performance. We illustrate our model by calculating remaining life expectancies and annuity values. We find that the husbands life expectancy at birth is generally increasing with his wifes age of death and the wifes life expectancy at birth is generally increasing with her husbands age of death. Ignoring the dependence between the remaining lifetimes of spouses may lead to an underestimation of the value of a joint annuity and an overestimation of the value of a single-life annuity, but less than suggested on the basis of the previous literature.",
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Estimating the joint survival probabilities of married individuals. / Sanders, Lisanne ; Melenberg, Bertrand.

In: Insurance: Mathematics & Economics, Vol. 67, 03.2016, p. 88-106.

Research output: Contribution to journalArticleScientificpeer-review

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AB - We estimate the joint survival probability of spouses using a large random sample drawn from a Dutch census. As benchmarks we use two bivariate Weibull models. We consider more flexible models, using a semi-nonparametric approach, by extending the independent Weibull distribution using squaredpolynomials. Also based on a nonparametric comparison, we find that extending the independent Weibull distribution by a squared third order polynomial shows the best performance. We illustrate our model by calculating remaining life expectancies and annuity values. We find that the husbands life expectancy at birth is generally increasing with his wifes age of death and the wifes life expectancy at birth is generally increasing with her husbands age of death. Ignoring the dependence between the remaining lifetimes of spouses may lead to an underestimation of the value of a joint annuity and an overestimation of the value of a single-life annuity, but less than suggested on the basis of the previous literature.

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