Academic Journal
Modeling trend processes in parametric mortality models.
| Τίτλος: | Modeling trend processes in parametric mortality models. |
|---|---|
| Συγγραφείς: | Börger, Matthias1, Schupp, Johannes1,2 j.schupp@ifa-ulm.de |
| Πηγή: | Insurance: Mathematics & Economics. Jan2018, Vol. 78, p369-380. 12p. |
| Θεματικοί όροι: | *Parametric modeling, *Mortality -- Mathematical models, Uncertainty, Longevity, Actuarial science |
| Περίληψη: | Parametric mortality models like those of Lee and Carter (1992) , Cairns et al. (2006), or Plat (2009) typically include one or more time dependent parameters. Often, a random walk with drift is used to project these parameters into the future. However, longer time series of historical mortality data often show patterns which a random walk with drift is highly unlikely to generate. In fact, historical mortality trends often appear to be trend stationary around piecewise linear trends with changing slopes over time (see, e.g., Sweeting (2011) or Li et al. (2011)). Periods of lower (but rather constant) mortality improvements are followed by periods of higher improvements and vice versa. In this paper, we propose an alternative trend process which builds on the patterns observed in the historical data. Future trend changes occur randomly over time, and also the trend change magnitude is stochastic. Furthermore, we show how the parameters of this trend process, in particular the probability of observing a trend change in a certain year and the distribution for the trend change magnitude, can be estimated from historical data. We also outline how uncertainty in the parameter estimates can be accounted for. Finally, we compare the trend process to other trend processes which have been proposed in the literature. [ABSTRACT FROM AUTHOR] |
| Copyright of Insurance: Mathematics & Economics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Business Source Index |
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| Items | – Name: Title Label: Title Group: Ti Data: Modeling trend processes in parametric mortality models. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Börger%2C+Matthias%22">Börger, Matthias</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Schupp%2C+Johannes%22">Schupp, Johannes</searchLink><relatesTo>1,2</relatesTo><i> j.schupp@ifa-ulm.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Insurance%3A+Mathematics+%26+Economics%22">Insurance: Mathematics & Economics</searchLink>. Jan2018, Vol. 78, p369-380. 12p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Parametric+modeling%22">Parametric modeling</searchLink><br />*<searchLink fieldCode="DE" term="%22Mortality+--+Mathematical+models%22">Mortality -- Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Uncertainty%22">Uncertainty</searchLink><br /><searchLink fieldCode="DE" term="%22Longevity%22">Longevity</searchLink><br /><searchLink fieldCode="DE" term="%22Actuarial+science%22">Actuarial science</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Parametric mortality models like those of Lee and Carter (1992) , Cairns et al. (2006), or Plat (2009) typically include one or more time dependent parameters. Often, a random walk with drift is used to project these parameters into the future. However, longer time series of historical mortality data often show patterns which a random walk with drift is highly unlikely to generate. In fact, historical mortality trends often appear to be trend stationary around piecewise linear trends with changing slopes over time (see, e.g., Sweeting (2011) or Li et al. (2011)). Periods of lower (but rather constant) mortality improvements are followed by periods of higher improvements and vice versa. In this paper, we propose an alternative trend process which builds on the patterns observed in the historical data. Future trend changes occur randomly over time, and also the trend change magnitude is stochastic. Furthermore, we show how the parameters of this trend process, in particular the probability of observing a trend change in a certain year and the distribution for the trend change magnitude, can be estimated from historical data. We also outline how uncertainty in the parameter estimates can be accounted for. Finally, we compare the trend process to other trend processes which have been proposed in the literature. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Insurance: Mathematics & Economics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.insmatheco.2017.09.024 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 369 Subjects: – SubjectFull: Parametric modeling Type: general – SubjectFull: Mortality -- Mathematical models Type: general – SubjectFull: Uncertainty Type: general – SubjectFull: Longevity Type: general – SubjectFull: Actuarial science Type: general Titles: – TitleFull: Modeling trend processes in parametric mortality models. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Börger, Matthias – PersonEntity: Name: NameFull: Schupp, Johannes IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 01676687 Numbering: – Type: volume Value: 78 Titles: – TitleFull: Insurance: Mathematics & Economics Type: main |
| ResultId | 1 |