Analysis of the Stochastic Mortality Models Based on Lee-Carter Model in Predicting Mortality Rates in Life and Health Insurance

Demographic indicators such as mortality rates play a very important role in health, financial and pension policies. Therefore, the accuracy of mathematical models in predicting death is an important challenge, and a more accurate prediction of life expectancy has an increasing impact on the policy-making of a large part of society. Therefore, the purpose of this study is to predict the mortality rate based on the family of stochastic mortality models and compare the results with each other.

One of the practical methods for predicting mortality is the Lee-Carter model. But this method, like other extrapolation methods, does not include information about the effects of medical, behavioral, or social advances on mortality rates. Among the generalizations of the Lee-Carter model are the Renshaw-Haberman and Currie models, which also apply age-specific cohort effects. In this study, a family of stochastic models is used to estimate model parameters, age-specific mortality rates and predict mortality rates. In this regard, human mortality database (HMD) data is used. But there is no information about our country in this database. Since the French mortality model is very close to the Iranian model and the life tables of this country (TD 88-90) are used in Iranian insurance applications, so the crude death rate of French men in the years 1900-2018 on the ages of 18, 40 and 65 years is used.

In this study, three different models of this family were evaluated. Based on the parameter estimation, the models fitted to the data and finally, the mortality rate prediction were found  that the Rinshaw-Haberman model performed better in predicting the mortality rate for all ages under study than the other two models.

In this study, by generalizing the Lee-Carter model by applying the applying the age-specific cohort effects, the performance of the model was improved and the optimal method was presented by evaluating these models.