• Communications for Statistical Applications and Methods
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• v.19 no.6
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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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• v.28 no.3
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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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• v.26 no.6
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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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• v.28 no.6
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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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• v.46 no.2
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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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• 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 Journal of Fisheries Business Administration
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• v.48 no.3
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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.

• The Journal of Fisheries Business Administration
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• v.47 no.4
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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.

• 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.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.