• Communications for Statistical Applications and Methods
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• 제19권6호
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• pp.859-868
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• 2012

Due to a rapidly aging society, the future Korea mortality rate is important for planning national financial strategies and social security policies. Old age mortality statistics are very limited in their ability to project a future mortality rate; therefore, it is essential to accurately estimate the old age mortality rate. In this paper, we show that the CK model with a Relational model as a base model provides accurate estimates of old age mortality rates.

• Communications for Statistical Applications and Methods
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• 제28권3호
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• pp.233-250
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• 2021

This paper studies if the accuracies of mortality models (LC model vs. 4-parametric model) are aggravated if a mortality structure changes due to the impact of COVID-19. LC model (LCM) uses dimension reduction for fitting to the log mortality matrix so that the performance of the dimension reduction method may not be good when the matrix structure changes. On the other hand, 4-parametric factor model (4-PFM) is designed to use factors for fitting to log mortality data by age groups so that it would be less affected by the change of the mortality structure. In fact, the forecast accuracies of LCM are better than those of 4-PFM when life-tables are used whereas those of 4-PFM are better when the mortality structure changes. Thus this result shows that 4-PFM is more reliable in performance to the structural changes of the mortality. To support the accuracy changes of LCM the functional aspect is explained by computing eigenvalues produced by singular vector decomposition

• Communications for Statistical Applications and Methods
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• 제26권6호
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• pp.557-573
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• 2019

Mortality study is an essential component of actuarial risk management for life insurance policies, annuities, and pension plans. Life expectancy has drastically increased over the last several decades; consequently, longevity risk associated with annuity products and pension systems has emerged as a crucial issue. Among the various aspects of mortality study, a consideration of the cause-of-death mortality can provide a more comprehensive understanding of the nature of mortality/longevity risk. In this case study, the cause-of-mortality data in Korea and the US were analyzed along with a multinomial logistic regression model that was constructed to quantify the impact of mortality reduction in a specific cause on actuarial values. The results of analyses imply that mortality improvement due to a specific cause should be carefully monitored and reflected in mortality/longevity risk management. It was also confirmed that multinomial logistic regression model is a useful tool for analyzing cause-of-death mortality for actuarial applications.

• Communications for Statistical Applications and Methods
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• 제28권6호
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• pp.611-626
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• 2021

Marital status has been identified as an important risk factor affecting adult mortality. Many studies have found that marriage has positive effects on mortality and increases life expectancy. Since most pension contracts providing retirement income are provided to married couples, mortality assumption for actuarial valuation based on the entire population is likely to overestimate the actual mortality of the group of beneficiaries specified in the contracts. This study considered the differences in mortality according to marital status to analyze the length and value of the payments of a typical pension contract for a married couple. The study quantified the effect on actuarial measurements of considering marital status in mortality assumptions with a multi-state model framework using Korean experience mortality data organized by marital status. The results of analysis indicate that considering marital status in mortality assumptions improves mortality risk management.

• Journal of Preventive Medicine and Public Health
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• 제46권2호
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• pp.74-81
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• 2013

Objectives: The objective of this study was to evaluate the performance of risk-adjusted mortality models for colorectal cancer surgery. Methods: We investigated patients (n=652) who had undergone colorectal cancer surgery (colectomy, colectomy of the rectum and sigmoid colon, total colectomy, total proctectomy) at five teaching hospitals during 2008. Mortality was defined as 30-day or in-hospital surgical mortality. Risk-adjusted mortality models were constructed using claims data (basic model) with the addition of TNM staging (TNM model), physiological data (physiological model), surgical data (surgical model), or all clinical data (composite model). Multiple logistic regression analysis was performed to develop the risk-adjustment models. To compare the performance of the models, both c-statistics using Hanley-McNeil pair-wise testing and the ratio of the observed to the expected mortality within quartiles of mortality risk were evaluated to assess the abilities of discrimination and calibration. Results: The physiological model (c=0.92), surgical model (c=0.92), and composite model (c=0.93) displayed a similar improvement in discrimination, whereas the TNM model (c=0.87) displayed little improvement over the basic model (c=0.86). The discriminatory power of the models did not differ by the Hanley-McNeil test (p>0.05). Within each quartile of mortality, the composite and surgical models displayed an expected mortality ratio close to 1. Conclusions: The addition of clinical data to claims data efficiently enhances the performance of the risk-adjusted postoperative mortality models in colorectal cancer surgery. We recommended that the performance of models should be evaluated through both discrimination and calibration.

• East Asian mathematical journal
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• 제35권3호
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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.

• 수산경영론집
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• 제48권3호
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• pp.47-59
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• 2017

Fish mortality is the most important success factor in aquaculture management. To order fingerlings considering the effect of mortality is a important problem in aquaculture farm. This study is aimed to decision the number and size of fry in aquaculture farm. This study build the mathematical model that finds the value of decision variable to minimize total cost that sums up the fingerling purchasing cost, aquaculture farm operating cost and feeding cost under mortality constraint. The proposed mathematical model involve biological and economical variables: (1) number of fingerlings (2) fish growth rate (3) mortality (4) price of a fry (5) feeding cost, and (6) possible order period. Numerical simulation model presented here in. The objective of numerical simulation is to provide for decision makers to analyse and comprehend the proposed model. When extensive biological and cost data become available, the proposed model can be widely applied to yield more accurate results.

• 수산경영론집
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• 제47권4호
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• pp.1-13
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• 2016

Fish mortality is the most important success factor in aquaculture management. To analyze the effect of mortality considering biological and economic condition is a important problem in land-based aquaculture. This study is aimed to analyze the effect of mortality for duration of cultivation in land-based aquaculture. This study builds the mathematical model that finds the value of decision variable to minimize cost that sums up the water pool usage cost, sorting cost, fingerling cost and feeding cost under critical standing corp constraint. The proposed mathematical model involves many aspects, both biological and economical: (1) number of fingerlings (2) timing and number of batch splitting event, based on (3) fish growth rate, (4) mortality, and (5) several farming expense. Numerical simulation model presented here in. The objective of numerical simulation is to provide for decision makers to analyse and comprehend the proposed model. When extensive biological and cost data become available, the proposed model can be widely applied to yield more accurate results.

• 응용통계연구
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• 제31권1호
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• pp.41-65
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• 2018

우리나라의 경우 선진국에 비해 짧은 기간 동안 사망률 개선이 급속히 이루어짐에 따라 사망률 예측에 있어 모형의 선택뿐만 아니라 시계열 이용기간의 선정 또한 중요한 고려사항이 될 수 있다. 따라서 본 연구에서는 시계열 이용기간의 선택 관점에서 회귀모형을 이용하는 방법을 제안하였다. 또한 Lee-Carter (LC) 모형, LC류 (Lee-Miller (LM), Booth-Maindonald-Smith (BMS)) 그리고 비모수 모형(functional data model (FDM), Coherent FDM)을 토대로 시계열 이용기간을 다르게 적용할 경우 어떠한 문제가 발생되며, 연령별 사망률과 기대수명 예측력에 어떠한 차이를 보이는지 살펴보았다. 분석결과를 바탕으로 5개의 모형별 2030년까지 남녀의 연령별 사망률과 예측기대수명을 작성하고 통계청(Korean Statistical Information Service; KOSIS)에서 제공하는 장래 연령별 사망률과 기대수명과 비교하였다.

• 응용통계연구
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• 제28권3호
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• pp.393-406
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• 2015

본 논문은 2요인(two-factor) 사망률 모형에 평균회귀모형(mean reverting process)을 적용하여 2요인의 확률적 변동을 모형화하여 사망률리스크(mortality risk)와 장수리스크(longevity risk)를 분석하였다. 최근 고령사회로 진입한 국가들에서 사망률 개선의 둔화가 관측되고 있는 시점에서 기존의 선형증가 또는 감소의 사망률 개선 모형을 보완함에 그 목적을 두었다. 영국의 1991~2015년 사망률 자료를 이용하여 제시한 모형의 모수를 메트로폴리스 알고리듬을 이용해 추정하였고 추정된 모수 값을 이용하여 다수 시뮬레이션을 통하여 장기간의 미래 사망률 예측값을 계산하였다. 평균회귀 모형의 특성으로 인해 약 60년의 시간이 지난 뒤부터는 사망률 개선이 거의 사라져 사망률이 일정한 값에 근접하였다. 사망률 개선이 둔화되는 현상이 관측되는 특정 집단(국가, 사회)의 경우 2요인 평균회귀 모형은 장기간 사망률 예측방법의 대안으로 간주될 것으로 기대되며, 모형의 응용으로서 평균회귀율의 추정결과로부터 사망률 개선의 속도를 계량화하는 기준을 제시하였다. 끝으로, 2014년~2040 기간의 사망률 예측값을 이용하여 25년 만기 장수채권의 발행가격을 산출하였다.