• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.393-406
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• 2015

We examine how to model mortality risk using the adaptation of the mean-reverting processes for the two factor model proposed by Cairns et al. (2006b). Mortality improvements have been recently observed in some countries such as United Kingdom; therefore, we assume long-run mortality converges towards a trend at some unknown time and the mean-reverting processes could therefore be an appropriate stochastic model. We estimate the parameters of the two-factor model incorporated with mean-reverting processes by a Metropolis-Hastings algorithm to fit United Kingdom mortality data from 1991 to 2015. We forecast the evolution of the mortality from 2014 to 2040 based on the estimation results in order to evaluate the issue price of a longevity bond of 25 years maturity. As an application, we propose a method to quantify the speed of mortality improvement by the average mean reverting times of the processes.

• Journal of Teachers' Pension
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• v.2
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• pp.181-206
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• 2017

출산율 하락과 기대여명 증가에 따라 인구구조의 고령화가 급격히 진행되고 있다. 이에 따라 소득보장이나 건강보장과 같은 사회보장제도의 장기 재정 불안정과 관련된 사회적 우려가 높다. 여러 세대를 거쳐 사회보장제도를 안정적으로 유지하기 위해서는 제도의 장기적 재정 상태에 대한 정확한 전망이 요청된다. 재정 상태에 대한 정확한 진단은 장기 재정 안정화를 위한 가장 기본적인 전제 조건이며, 정확한 재정 상태에 대한 평가 없이 재정 안정화를 위한 사회적 합의를 도출하는 것은 가능하지 않다. 본 연구는 사학연금의 장기 재정 전망에 필요한 사망률 전망 방법을 검토함으로써 사학연금 장기 재정 전망 작업의 정확성과 신뢰성을 높이고자 하는 목적을 가지고 있다. 보다 구체적으로, 본 연구는 연앙인구 및 사망 건수 자료가 제한적인 동시에 단기 시계열 자료만이 존재하는 사학연금 데이터베이스의 특성을 반영한 사망률 전망 모형을 구축하고 있다. 사학연금 남성 사망률 전망과 관련하여 본 연구에서 제안하는 모형은 목표 집단의 사망력 패턴과 밀접히 연관된 준거 집단을 통합적으로 모형화하는 정합적 사망률 모형(coherent mortality model)이다. 반면 관측된 사망 건수가 매우 제한적인 관계로 사학연금 데이터베이스에 기초하여 사망률을 전망하기 쉽지 않은 여성 사망률의 경우 통계청 장래인구추계에서 전망된 성별 사망확률 격차가 사학연금에도 적용될 수 있다는 가정하에 사학연금 여성 사망률을 전망하는 방법을 제안하고 있다.

• The Korean Journal of Applied Statistics
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• v.34 no.3
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• pp.347-373
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• 2021

Over the past 50 years, explorative research on the nation's mortality decline patterns has showed a decrease in age-specific mortality rates in all age groups, but there were different improvement patterns in specific mortality rates depending on ages and periods. Greater distinct improvement was observed in mortality rates among women than men, and there was a noticeable improvement in mortality rates in certain groups especially in the more recent decades, revealing a structural change in the overall trends regarding death periods. In this paper, we compare various stochastic mortality models considering cohort effects for mortality projection using Korean female mortality data and further explore the uncertainty related to projection. It also created age-specific mortality rates and life expectancy for women until 2067 based on the results of the analysis, and compared them with future age-specific mortality rates and life expectancy provided by the national statistical office (KOISIS). The best optimal model could vary depending on data usage periods. however, considering the overall fit and predictability, the PLAT model would be regarded to have appropriate predictability in terms of the mortality rates of women in South Korea.

• 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.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.

• 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.

• The Korean Journal of Applied Statistics
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• v.28 no.4
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• pp.703-719
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• 2015

We propose an extension of the Lee and Jho (2015) mean reverting the two factor mortality model by incorporating a period-specific cohort effect. We found that the consideration of cohort effect improves the mortality fit of Korea male data above age 65. Parameters are estimated by the weighted least squares method and Metropolis algorithm. We also emphasize that the cohort effect is necessary to choose the base survival index to calculate longevity bond issue price. A key contribution of the article is the proposal and development of a method to calculate the longevity bond price to hedge the longevity risk exposed to Korea National Pension Services.

• Journal of Digital Convergence
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• v.11 no.5
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• pp.371-384
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• 2013

The purpose of this study was to develop the risk-adjusted mortality model using Korean Hospital Discharge Injury data and US National Hospital Discharge Survey data and to suggest some ways to manage hospital mortality rates through comparison of Korea and United States Hospital Standardized Mortality Ratios(HSMR). This study used data mining techniques, decision tree and logistic regression, for developing Korea and United States risk-adjustment model of in-hospital mortality. By comparing Hospital Standardized Mortality Ratio(HSMR) with standardized variables, analysis shows the concrete differences between the two countries. While Korean Hospital Standardized Mortality Ratio(HSMR) is increasing every year(101.0 in 2006, 101.3 in 2007, 103.3 in 2008), HSMR appeared to be reduced in the United States(102.3 in 2006, 100.7 in 2007, 95.9 in 2008). Korean Hospital Standardized Mortality Ratios(HSMR) by hospital beds were higher than that of the United States. A two-aspect approach to management of hospital mortality rates is suggested; national and hospital levels. The government is to release Hospital Standardized Mortality Ratio(HSMR) of large hospitals and to offer consulting on effective hospital mortality management to small and medium hospitals.

• 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.