Lifetime dependence modelling using a truncated multivariate gamma distribution
| Autor: | Zinoviy Landsman, Daniel H. Alai, Michael Sherris |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Statistics and Probability
Economics and Econometrics Longevity risk business.industry Matrix gamma distribution Method of moments (probability theory) Law of large numbers Life insurance Econometrics Portfolio Statistics Probability and Uncertainty Valuation (measure theory) business Risk management Mathematics |
| Zdroj: | Insurance: Mathematics and Economics. 52:542-549 |
| ISSN: | 0167-6687 |
| DOI: | 10.1016/j.insmatheco.2013.03.011 |
| Popis: | Systematic improvements in mortality increases dependence in the survival distributions of insured lives, which is not accounted for in standard life tables and actuarial models used for annuity pricing and reserving. Systematic longevity risk also undermines the law of large numbers, a law that is relied on in the risk management of life insurance and annuity portfolios. This paper applies a multivariate gamma distribution to incorporate dependence. Lifetimes are modelled using a truncated multivariate gamma distribution that induces dependence through a shared gamma distributed component. Model parameter estimation is developed based on the method of moments and generalized to allow for truncated observations. The impact of dependence within a portfolio, or cohort, of lives with similar risk characteristics is demonstrated by applying the model to annuity valuation. Dependence is shown to have a significant impact on the risk of the annuity portfolio as compared with traditional actuarial methods that implicitly assume independent lifetimes. |
| Databáze: | OpenAIRE |
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