• 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.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.171-188
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• 2021

Due to an increased demand for longevity risk analysis, various stochastic models have been suggested to evaluate uncertainly in estimated life expectancy and the associated value of future annuity payments. Recently updated data allow us to analyze mortality for a longer historical period and extended age ranges. This study followed up previous case studies using up-to-date empirical data on Korean mortality and the recently developed R package StMoMo for stochastic mortality models analysis. The suitability of stochastic mortality models, focusing on retirement ages, was investigated with goodness-of-fit, validity of models, and ability of generating reasonable sets of simulation paths of future mortality. Comparisons were made across various types of models. Based on the selected models, the variability of important estimated measures associated with pension, annuity, and reverse mortgage were quantified using simulations.

• The Korean Journal of Applied Statistics
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• v.23 no.4
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• pp.651-668
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• 2010

Various estimators of two risk measures of a specific financial portfolio, Value-at-Risk and Expected Shortfall, are compared for each case of 1-day and 10-day horizons. We use the Korea Composite Stock Price Index data of 20-year period including the year 2008 of the global financial crisis. Indexes of five foreign stock markets are also used for the empirical comparison study. The estimator considering both the heavy tail of loss distribution and the conditional heteroscedasticity of time series is of main concern, while other standard and new estimators are considered too. We investigate which estimator is best for the Korean stock market and which one shows the best overall performance.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1315-1331
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• 2014

Replacement rates which shows the ratio of retirement income relative to preretirement income is used for a valuable evaluation measures while discussing social security benefit levels or the adequacy of retirement income. However, replacement rates has been only used for an index for evaluating benefit level at the time of retirement or specific retirement period in advanced research projects. This article analyzes how much the uncertainty of survival has an influence on retirement income, and shows replacement rates in conformity with the period of survival as an index. The researchers named this index lifetime income replacement rates. Analysis based on this index shows both life replacement income rates of 38.3% in men's case and of 41.1% in women's case while enrolled for 20years in three pension plans - national pension, retirement pension and individual annuity.

• The Korean Journal of Applied Statistics
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• v.34 no.5
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• pp.761-772
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• 2021

Simulation results for the comparison of estimators of interest are usually reported in tables or plots. However, if the simulations are conducted under various conditions for many estimators, the comparison can be difficult to be made with tables or plots. Furthermore, for algorithms that take a long time to run, the number of iterations of the simulation is costly to to be increased. The analysis of simulation results using regression models allows us to compare the estimators more systematically and effectively. Since variances in performance measures may vary depending on the simulation conditions and estimators, the heteroscedasticity of the error term should be allowed in the regression model. And multiple comparisons should be made because multiple estimators should be compared simultaneously. We introduce background theories of heteroscedasticity and multiple comparisons in the context of analyzing simulation results. We also present a concrete example.

• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.445-452
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• 2009

Credibility models are actuarial tools to distribute premiums fairly among a heterogeneous group of policyholders. Many existing credibility models can be expressed as special cases of linear mixed effects models. In this paper we propose a nonlinear credibility regression model by reforming the linear mixed effects model through kernel machine. The proposed model can be seen as prediction method applicable in any setting where repeated measures are made for subjects with different risk levels. Experimental results are then presented which indicate the performance of the proposed estimating procedure.

• Communications for Statistical Applications and Methods
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• v.25 no.2
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• pp.185-197
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• 2018

Measuring market fear is an important way of understanding fundamental economic phenomena related to financial crises. There have been several approaches to measure market fear or panic level in a financial market. Recently, herd behavior has gained its popularity as important economic phenomena explaining the fear in the financial market. In this paper, we investigate herd behavior in global stock markets with a focus on intercontinental comparison. While various risk measures are available for the detection of herd behavior in the market, we use the standardized herd behavior index in Dhaene et al. (Insurance: Mathematics and Economics, 50, 357-370, 2012b) and Lee and Ahn (Dependence Modeling, 5, 316-329, 2017) for the comparison of herd behaviors in global stock markets. A global stock market data from Morgan Stanley Capital International is used to study herd behavior especially during periods of financial crises.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.65-83
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• 2022

Although various statistical methods have been developed to map time-dependent genetic factors, most identified genetic variants can explain only a small portion of the estimated genetic variation in longitudinal traits. Gene-gene and gene-time/environment interactions are known to be important putative sources of the missing heritability. However, mapping epistatic gene-gene interactions is extremely difficult due to the very large parameter spaces for models containing such interactions. In this paper, we develop a Gaussian process (GP) based nonparametric Bayesian variable selection method for longitudinal data. It maps multiple genetic markers without restricting to pairwise interactions. Rather than modeling each main and interaction term explicitly, the GP model measures the importance of each marker, regardless of whether it is mostly due to a main effect or some interaction effect(s), via an unspecified function. To improve the flexibility of the GP model, we propose a novel grid-based method for the within-subject dependence structure. The proposed method can accurately approximate complex covariance structures. The dimension of the covariance matrix depends only on the number of fixed grid points although each subject may have different numbers of measurements at different time points. The deviance information criterion (DIC) and the Bayesian predictive information criterion (BPIC) are proposed for selecting an optimal number of grid points. To efficiently draw posterior samples, we combine a hybrid Monte Carlo method with a partially collapsed Gibbs (PCG) sampler. We apply the proposed GP model to a mouse dataset on age-related body weight.

• The Korean Journal of Applied Statistics
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• v.28 no.4
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• pp.721-739
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• 2015

The importance of the old age income security will increase for an aging society due to the deepening income polarization. The National Pension(NP) is a representative Social Security scheme in charge of old age income security as well as income redistribution for the insured. Studies by Kim (2002), Kim et al. (2003), and Hong (2013) have reported the possibility of unsatisfactory income redistribution of the NP. Recently Choi (2015) attributed those results to an unnoticed defect in the benefit formula. This study is a test for the unsatisfactory income redistribution of the current National Pension using early participants who have now become pensioners. The method aggregates cohorts and combines individual history data before the year 2013 and the results of the actuarial projection model of the 2013 after the year 2014. The results are divided by measures taken. The redistribution is obviously progressive by the income replacement rate; however, it is significantly regressive when measured by the net benefit theoretically as more plausible. Considering the effect of differing lifetime contribution year among income classes, the regressive redistribution will prevail more in the future pensioners.