Bayesian graduation of mortality rates: An application to reserve evaluation |
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Authors: | Csar da Rocha Neves Helio S Migon |
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Institution: | aUniversidade Federal do Rio de Janeiro, COPPE, PO Box 68507, CEP: 21945970, Rio de Janeiro, Brazil;bUniversidade Federal do Rio de Janeiro, Instituto de Matematica e COPPE, PO Box - 68507, 21945970 Rio de Janeiro, Brazil |
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Abstract: | This paper presents Bayesian graduation models of mortality rates, using Markov chain Monte Carlo (MCMC) techniques. Graduated annual death probabilities are estimated through the predictive distribution of the number of deaths, which is assumed to follow a Poisson process, considering that all individuals in the same age class die independently and with the same probability. The resulting mortality tables are formulated through dynamic Bayesian models. Calculation of adequate reserve levels is exemplified, via MCMC, making use of the value at risk concept, demonstrating the importance of using “true” observed mortality figures for the population exposed to risk in determining the survival coverage rate. |
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Keywords: | Bayesian graduation Dynamic models Predictive distribution MCMC Bayesian mortality table Mathematical reserve Value at risk |
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