• East Asian mathematical journal
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• v.35 no.3
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• pp.305-318
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• 2019

Over the past decades, the Lee-Carter model [1] has attracted much attention from various demography-related fields in order to project the future mortality rates. In the Lee-Carter model, the speed of mortality improvement is stochastically modeled by the so-called mortality index and is used to forecast the future mortality rates based on the time series analysis. However, the modeling is applied to long time series and thus an important structural change might exist, leading to potentially large long-term forecasting errors. Therefore, in this paper, we are interested in detecting the structural change of the Lee-Carter model and investigating the actuarial implications. For the purpose, we employ the tests proposed by Coelho and Nunes [2] and analyze the mortality data for six countries including Korea since 1970. Also, we calculate life expectancies and whole life insurance premiums by taking into account the structural change found in the Korean male mortality rates. Our empirical result shows that more caution needs to be paid to the Lee-Carter modeling and its actuarial applications.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.41-59
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• 2016

There have been continuous improvements in human life expectancy. Life expectancy is as a key factor in an aging population and can wreak severe damage on the financial integrity of pension providers. Hence, the projection of the accurate future mortality is a critical point to prevent possible losses to pension providers. However, improvements in future mortality would be overestimated by a typical mortality projection method using the Lee-Carter model since it underestimates the mortality index ${\kappa}_t$. This paper suggests a mortality projection based on the projection of the skewness of the mortality versus the typical mortality projection of the Lee-Carter model based on the projection of the mortality index, ${\kappa}_t$. The paper shows how to indirectly estimate future t trend with the skewness of the mortality and compares the results under each estimation method of the mortality index, ${\kappa}_t$. The analysis of the results shows that mortality projection based on the skewness presents less improved mortality at an elderly ages than the original projection.

• The Korean Journal of Applied Statistics
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• v.31 no.5
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• pp.637-653
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• 2018

Rapid aging of the population affects population structure and population aging. Consequently, developed countries have focused on population aging as a major issue in regards to pension sustainability finances as well as health and the elderly welfare system. Mortality projections that result from population structure changes and population aging are increasingly important. This paper compares six mortality models using KOSTAT's life table from 1970 to 2016. The models are rooted in the Lee-Carter (LC) model (Lee and Carter, Journal of the American Statistical Association, 87, 659-671, 1992) and have been modified and improved on the assumptions of the LC model. We examined the improvement process and the check assumption by models in order to find a suitable mortality model for Korea. Korea shows rapid aging and declined mortality rate by age; therefore, it is desirable to estimate and predict mortality from LL&LC-ER models by combining LC-ER, LL, and LC-ER models that reflect the phenomena and modify age-specific mortality patterns without major changes in expected life expectancy.

• The Korean Journal of Applied Statistics
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• v.18 no.3
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• pp.639-654
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• 2005

The Lee and Carter method has widely used to forecast mortality because of the simple structure of model and the stable forecasting. The Lee and Carter method, however, also has limitations. The assumption of the rate of decline in mortality at each age remaining invariant over time has been violated in several decades. And, there is no way to include covariates in the model for better forecasts. Here we introduce Park, Choi and Kim method to make up for Lee and Carter's weak points by using two random processes. We discuss structural features of two methods. furthermore, for each method, we forecast life expectancy for 2005 to 2050 using South Korea data and compare the results.

• The Korean Journal of Applied Statistics
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• v.31 no.1
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• pp.41-65
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• 2018

In Korea, as the mortality rate improves in a shorter period of time than in developed countries, it is important to consider the selection of the time series as well as the model selection in the mortality projection. Therefore, this study proposed a method using the multiple regression model in respect to the selection of the time series period. In addition, we investigate the problems that arise when various time series are used based on the Lee-Carter (LC) model, the kinds of LC model along with Lee-Miller (LM) and Booth-Maindonald-Smith (BMS), and the non-parametric model such as functional data model (FDM) and Coherent FDM, and examine differences in the age-specific mortality rate and life expectancy projection. Based on the analysis results, the age-specific mortality rate and predicted life expectancy of men and women are calculated for the year 2030 for each model. We also compare the mortality rate and life expectancy of the next generation provided by Korean Statistical Information Service (KOSIS).

• The Korean Journal of Applied Statistics
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• v.31 no.1
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• pp.77-96
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• 2018

A reverse mortgage provides a pension until the death for the insured or last survivor. Long-term risk management is important to estimate the contractual period of a reverse mortgage. It is also necessary to study prediction methods of mortality rates that appropriately reflect the improvement trend of the mortality rate since the extension of the life expectancy, which is the main cause of aging, can have a serious impact on the pension financial soundness. In this study, the Lee-Carter (LC) model reflects the improvement in mortality rates; in addition, multiple life model are also applied to a reverse mortgage. The mortality prediction method by the traditional LC model has shown a dramatic improvement in the mortality rate; therefore, this study suggests mortality projection based on the projection of the skewness for the mortality that has been applied to appropriately reflect the improvement trend of the mortality rate. This paper calculates monthly payments using future mortality rates based on the projection of the skewness of the mortality. As a result, the mortality rates based on this method less reflect the mortality improvement effect than the mortality rates based on a traditional LC model and a larger pension amount is calculated. In conclusion, this method is useful to forecast future mortality trend results in a significant reduction of longevity risk. It can also be used as a risk management method to pay appropriate monthly payments and prevent insufficient payment due to overpayment by the issuing institution and the guarantee institution of the reverse mortgage.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.521-536
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• 2021

As life expectancies increase continuously over the world, the accuracy of forecasting mortality is more and more important to maintain social systems in the aging era. Currently, the most popular model used is the Lee-Carter model but various studies have been conducted to improve this model with one of them being 6-parametric factor model (6-PFM) which is introduced in this paper. To this new model, long short-term memory (LSTM) and regularized LSTM are applied in addition to vector autoregression (VAR), which is a traditional time-series method. Forecasting accuracies of several models, including the LC model, 4-PFM, 5-PFM, and 3 6-PFM's, are compared by using the U.S. and Korea life-tables. The results show that 6-PFM forecasts better than the other models (LC model, 4-PFM, and 5-PFM). Among the three 6-PFMs studied, regularized LSTM performs better than the other two methods for most of the tests.

• Korea journal of population studies
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• v.29 no.2
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• pp.27-51
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• 2006

In this paper, I have tested various kinds of methods for mortality projection and chose Lee-Carter method for projection of Korean mortality by age and sex. I reviewed the trends of life tables and life expectancies by age and sex from 2005 to 2050 projected by Lee-Carter method and found that the method was very applicable for Korean mortality projection. The differences between reported and estimated data for the period of 1971-2003 were small enough for both sexes and for all of the age groups. The projected life expectancies in 2051 were 82.73 years for males and 89.41 for females, and the differences decreased from 7.06 years in 2005 to 6.68 years. Because of the limitation of Korean infant mortality rate, I adopted the Japanese estimated IMR in 2050 as Korean object level in 2051. When the time series of IMR become long enough, we can use Korean IMR directly for the mortality projection. In addition, if we can estimate the changes of the main cause of death correctly in future, the mortality projection will be more correct and reliable. This will be available when we can produce a long series of life tables by cause of deaths.

• Proceedings of the Korean Statistical Society Conference
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• 2005.11a
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• pp.49-53
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• 2005

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.115-125
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• 2011

By use of a mortality forecasting model and a life table, forecasting the average life expectancy is an effective way to evaluate the future mortality level. There are differences between the actual values of average life expectancy at present and the forecasted values of average life expectancy in population projection 2006 from Statistics Korea. The reason is that the average life expectancy forecasts did not reflect the increasing speed of the actual ones. The main causes of the problem may be errors from judgment for projection, from choice, or use of a mortality forecasting model. In this paper, we focus on the choice of the mortality forecasting model to inspect this problem. Statistics Korea should take a mortality forecasting model with considerable investigation to proceed population projection 2011 without the errors observed in population projection 2006. We compare the five mortality forecasting models that are the LC(Lee and Carter) model used widely and its variants, and the HP8(Heligman and Pollard 8 parameter) model for handling death probability. We make average life expectancy forecasts by sex using modeling results from 2010 to 2030 and compare with that of the population projection 2006 during the same period. The average life expectancy from all five models are forecasted higher than that of the population projection 2006. Therefore, we show that the new average life expectancy forecasts are relatively suitable to the future mortality level.