Correlated age-specific mortality model: an application to annuity portfolio management
type: Item
instance of: scholarly article
title: Correlated age-specific mortality model: an application to annuity portfolio management
zbMATH Open document ID: 1482.91184
author: Tzuling Lin
author: Chou-Wen Wang
author: Cary Chi-Liang Tsai
published in: European Actuarial Journal
publication date: 2022-01-14T00:00:00Z
review text: In this paper, the authors discuss the modelling of the dynamics of age-specific incremental mortality using a stochastic process with the objective of incorporating mortality correlations across ages. Specifically, they model the drift rate as the average annual improvement rate of a group time trend for all ages and consider both normal and non-normal distributions for the distribution of residuals. Some key features such as skewness, heavy-tailedness, jumps are captured in the non-normal residual distributions. To incorporate the inter-age mortality dependence, the authors employ a one-factor copula model with six distributions. Applications of the proposed models to pricing and quantifying risks of three annuity portfolios are provided. Specifically, the authors propose approximations to the change in the value of an annuity portfolio with respect to a proportional or constant change in the force of mortality. They also consider the estimation of value at risk (VaR) and some summary statistics, say the mean, variance, skewness, kurtosis, of the loss distribution for each of the three annuity portfolios. The specification of the proposed age-specific mortality model is presented in Section 2. Section 2.1 introduces three approaches for the estimation of annual drift rates of the logarithmic forces of mortality. Section 2.2 discusses several non-normal distributions, say a jump-diffusion distribution, a Student's t distribution, a normal inverse Gaussian distribution and a variance Gamma distribution, for the residuals. Section 3 presents the one-factor copula model, where the latent variables for different ages depend on one common factor and an idiosyncratic factor independent of the common factor. A copula function is then used to modelling the dependency of the latent variables for different ages. Six pairs of distributions for the common factor and the idiosyncratic factor are considered. In Section 4, the models are fitted to mortality data for both genders …
reviewed by: Tak Kuen Siu
Mathematics Subject Classification ID: 91G05
Mathematics Subject Classification ID: 91D20
Mathematics Subject Classification ID: 62P05
zbMATH DE Number: 7457619
zbMATH Keywords: stochastic mortality model
zbMATH Keywords: copula
zbMATH Keywords: mortality dependence
zbMATH Keywords: annuity portfolio
MaRDI profile type: Publication
full work available at URL: s13385-021-00269-y
OpenAlex ID: W3135671680
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DOI: 10.1007/S13385-021-00269-Y
description: scientific article; zbMATH DE number 7457619