• 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.

• 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.

• 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.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.

• Journal of the Korean Data and Information Science Society
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• v.24 no.3
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• pp.571-584
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• 2013

Various risk factors other than age and sex affecting human mortality have been identified and quantitatively analyzed by previous studies in many area of research. Marital status is one of key mortality risk factors which affect life expectancy directly or indirectly. Relevant results have implication on risk management for both of social and private insurance. In this paper, a mortality model to reflect mortality differential according to marital status and possible transitions among marital status is designed. Various actuarial calculations were performed and related issues were discussed.

• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.655-671
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• 2021

This study analyzes the premium risk of insurers in Korea, which is expected to experience the fastest population aging in the world. Based on the Lee-Carter model, we generate 10,000 scenarios for the number of future survivors in the group of the 10,000 policyholders of life annuity. According to the result of simulation study, the probability of insurer's loss for both groups of male and female policyholders is very low. This result indicates that the premium risk of insurers is not as great as the insurer's concern. This study also suggests introduction of the longevity swap as an alternative to manage the premium risk for the insurer which sells life annuity products. The longevity swap allows insurers to hedge premium risk and reduce capital burden due to the premium risk inherent in life annuity. This study also shows through examples that the counterparty of swap deal may have excess profit in exchange for taking premium risk.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.79-95
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• 2020

The globalization of financial markets has broadened investment opportunities. International investors' investment portfolios consist of financial instruments from various countries; consequently, the risks associated with economic dependence among countries should be carefully considered. Step-down equity-linked securities (ELS) are a structured financial product that have recently become popular among Korean investors. Payoffs are based on two or three stock indices from different regions; therefore, dependence between the indices should be reflected in the risk analysis. In this study, we consider a regime-switching copula model to describe the joint behavior of two stock indices- the Eurostoxx50 and the Hang Seng China Enterprises Index (HSCEI). These indices are commonly used as underlying assets of step-down ELS. Using historical data, we analyze the risk associated with step-down ELS through the probabilities of early redemption. A regime-switching copula model can accommodate complicated dependence. Thus, it should be considered in the risk analysis of step-down ELS.

• Communications for Statistical Applications and Methods
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• v.31 no.3
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• pp.323-336
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• 2024

The accurate forecasting of insurance claims is a critical component for insurers' risk management decisions. Hierarchical Bayesian parametric (BP) models can be used for health insurance claims forecasting, but they are unsatisfactory to describe the claims distribution. Therefore, Bayesian nonparametric (BNP) models can be a more suitable alternative to deal with the complex characteristics of the health insurance claims distribution, including heavy tails, skewness, and multimodality. In this study, we apply both a BP model and a BNP model to predict group health claims using simulated and real-world data for a private life insurer in Indonesia. The findings show that the BNP model outperforms the BP model in terms of claims prediction accuracy. Furthermore, our analysis highlights the flexibility and robustness of BNP models in handling diverse data structures in health insurance claims.

• Communications for Statistical Applications and Methods
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• v.27 no.6
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• pp.675-688
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• 2020

In survival analysis of observational data, the inverse probability weighting method and the Cox proportional hazards model are widely used when estimating the causal effects of multiple-valued treatment. In this paper, the two kinds of weights have been examined in the inverse probability weighting method. We explain the reason why the stabilized weight is more appropriate when an inverse probability weighting method using the generalized propensity score is applied. We also emphasize that a marginal hazard ratio and the conditional hazard ratio should be distinguished when defining the hazard ratio as a treatment effect under the Cox proportional hazards model. A simulation study based on real data is conducted to provide concrete numerical evidence.

• Communications for Statistical Applications and Methods
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• v.29 no.6
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• pp.679-694
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• 2022

Mortality risk is a significant threat to individual life, and quantifying the risk is necessary for making a national population plan and is a traditionally fundamental task in the insurance and annuity businesses. Like other advanced countries, the sustainability of life pensions and the management of longevity risks are becoming important in Asian countries entering the era of aging society. In this study, mortality and pension value sustainability trends are compared and analyzed based on national population and mortality data, focusing on four Asian countries from 1990 to 2017. The result of analyzing the robustness and accuracy of generalized linear/nonlinear models reveals that the Cairns-Blake-Dowd model, the nonparametric Renshaw-Haberman model, and the Plat model show low stability. The Currie, CBD M5, M7, and M8 models have high stability against data periods. The M7 and M8 models demonstrate high accuracy. The longevity risk is found to be high in the order of Taiwan, Hong Kong, Korea, and Japan, which is in general inversely related to the population size.