Forecasting Models/ Time Series
Shirin Shoaee; Mohammad Mehdi Gholi Keshmarzi
Abstract
Purpose: Mortality is a dynamic process that completes over time and is a fundamental issue in life insurance, pension fund, health insurance, and in general any issue related to financial planning that deals with the longevity of individuals. Therefore, the accuracy of mathematical models in predicting ...
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Purpose: Mortality is a dynamic process that completes over time and is a fundamental issue in life insurance, pension fund, health insurance, and in general any issue related to financial planning that deals with the longevity of individuals. Therefore, the accuracy of mathematical models in predicting mortality rates is an important challenge. The purpose of this study is to generalize static stochastic mortality models to dynamic stochastic mortality models and to predict mortality rates based on the generalization of stochastic mortality models by the Cox-Ingersoll-Ross (CIR) process and to compare the results with each other.Methodology: In this research, two suggestions are presented: the first idea is to provide a dynamic correction method to increase the prediction accuracy using the CIR process and the second idea is to examine the out-of-sample validation method.Findings: In this study, using the out-of-sample validation method, the force of mortality from the best models selected from the two famous mortality model families (Lee-Carter and Cairns, Blake and Dowd (CBD)) is compared with the results of the generalized model. After estimating the parameters of the studied models and calculating the prediction of the mortality rates, by calculating the mean absolute error and root mean squares error of prediction, it is determined that the generalization of stochastic mortality models by the CIR process performs much better than static mortality models. The Bayesian information criterion also indicates that the use of generalized stochastic mortality models is justified.Originality/Value: In this study, stochastic mortality index models, which include Lee-Carter and Cairns-Blake-Dowd family models, are used and generalized by the CIR process. In this regard, Human Mortality Database (HMD) data is used. But there is no information about our country in this database. Because the French mortality pattern is very close to the Iranian pattern and the life tables of this country (TD 88-90) are used in Iranian insurance applications, the crude death rate of French men in the years 1900-2018 on the ages of 18, 40 and 65 years is used. Using these data and the backtesting method, static mortality models and generalized models with the CIR process are compared.