• Communications for Statistical Applications and Methods
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• v.27 no.3
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• pp.327-347
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• 2020

We consider a credit portfolio with highly skewed exposures. In the portfolio, small number of obligors have very high exposures compared to the others. For the Bernoulli mixture model with highly skewed exposures, we propose a new importance sampling scheme to estimate the tail loss probability over a threshold and the corresponding expected shortfall. We stratify the sample space of the default events into two subsets. One consists of the events that the obligors with heavy exposures default simultaneously. We expect that typical tail loss events belong to the set. In our proposed scheme, the tail loss probability and the expected shortfall corresponding to this type of events are estimated by a conditional Monte Carlo, which results in variance reduction. We analyze the properties of the proposed scheme mathematically. In numerical study, the performance of the proposed scheme is compared with an existing importance sampling method.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1201-1212
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• 2016

Value at Risk (VaR) for market risk management is a favorite method used by financial companies; however, there are some problems that cannot be explained for the amount of loss when a specific investment fails. Conditional Tail Expectation (CTE) is an alternative risk measure defined as the conditional expectation exceeded VaR. Multivariate loss rates are transformed into a univariate distribution in real financial markets in order to obtain CTE for some portfolio as well as to estimate CTE. We propose multivariate CTEs using multivariate quantile vectors. A relationship among multivariate CTEs is also derived by extending univariate CTEs. Multivariate CTEs are obtained from bivariate and trivariate normal distributions; in addition, relationships among multivariate CTEs are also explored. We then discuss the extensibility to high dimension as well as illustrate some examples. Multivariate CTEs (using variance-covariance matrix and multivariate quantile vector) are found to have smaller values than CTEs transformed to univariate. Therefore, it can be concluded that the proposed multivariate CTEs provides smaller estimates that represent less risk than others and that a drastic investment using this CTE is also possible when a diversified investment strategy includes many companies in a portfolio.

• Communications for Statistical Applications and Methods
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• v.29 no.1
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• pp.85-101
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• 2022

Derivative-linked securities (DLS) is a type of derivatives that offer an agreed return when the underlying asset price moves within a specified range by the maturity date. The underlying assets of DLS are diverse such as interest rates, exchange rates, crude oil, or gold. A German 10-year bond rate-linked DLS and a USD-GBP CMS rate-linked DLS have recently become a social issue in Korea due to a huge loss to investors. In this regard, this paper accounts for the payoff structure of these products and evaluates their prices and fair coupon rates as well as risk measures such as Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR). We would like to examine how risky these products were and whether or not their coupon rates were appropriate. We use Hull-White Model as the stochastic model for the underlying assets and Monte Carlo (MC) methods to obtain numerical results. The no-arbitrage prices of the German 10-year bond rate-linked DLS and the USD-GBP CMS rate-linked DLS at the center of the social issue turned out to be 0.9662% and 0.9355% of the original investment, respectively. Considering that Korea government bond rate for 2018 is about 2%, these values are quite low. The fair coupon rates that make the prices of DLS equal to the original investment are computed as 4.76% for the German 10-year bond rate-linked DLS and 7% for the USD-GBP CMS rate-linked DLS. Their actual coupon rates were 1.4% and 3.5%. The 95% VaR and TVaR of the loss for German 10-year bond rate-linked DLS are 37.30% and 64.45%, and those of the loss for USD-GBP CMS rate-linked DLS are 73.98% and 87.43% of the initial investment. Summing up the numerical results obtained, we could see that the DLS products of our interest were indeed quite unfavorable to individual investors.

• The Korean Journal of Financial Management
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• v.23 no.2
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• pp.189-208
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• 2006

In this paper we are concerned with estimation of tail related risk measures for heteroscedastic financial time series and VaR limits that VaR tells us nothing about the potential size of the loss given. So we use GARCH-EVT model describing the tail of the conditional distribution for heteroscedastic financial series and adopt Expected Shortfall to overcome VaR limits. The main results can be summarized as follows. First, the distribution of stock return series is not normal but fat tail and heteroscedastic. When we calculate VaR under normal distribution we can ignore the heavy tails of the innovations or the stochastic nature of the volatility. Second, GARCH-EVT model is vindicated by the very satisfying overall performance in various backtesting experiments. Third, we founded the expected shortfall as an alternative risk measures.

• Communications for Statistical Applications and Methods
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• v.19 no.2
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• pp.267-276
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• 2012

Bagai et al. (1989) proposed a distribution-free test for stochastic ordering in the competing risk model, and recently Murakami (2009) utilized a standard saddlepoint approximation to provide tail probabilities for the Bagai statistic under finite sample sizes. In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic. We make numerical comparisons of these approximations for moderate sample sizes as was done in Murakami (2009). From the numerical results, it was observed that the Gaussianpolynomial approximation provides comparable or greater accuracy in the tail probabilities than the saddlepoint approximation. Unlike saddlepoint approximation, the Gaussian-polynomial approximation provides a simple explicit representation of the approximated density function. We also discuss the details of computations.

• Proceedings of the KSR Conference
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• 2007.05a
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• pp.1107-1112
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• 2007

This study reviews the work that has been carried out to date on the effects of train slipstreams, which begins as the head of the train passes and continues until after the tail of the train passed, on people and their belongings on station platforms. Recorded incidents in UK involving station users and their property on station platforms caused by train slipstreams are reviewed. Methods used by other railway administrations to manage the risk from slipstream effects on station platforms are described. Recommendations to improve the platform design of the risk are made. The extent to which design guides for assessing the risk can be developed is considered.

• Communications for Statistical Applications and Methods
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• v.13 no.2
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• pp.389-407
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• 2006

Extreme value theory has been used widely in many areas of science and engineering to deal with the assessment of extreme events which are rare but have catastrophic consequences. The potential of extreme value theory has only been recognized recently in finance area. In this paper, we provide an overview of extreme value theory for estimating and assessing value at risk and expected shortfall which are the methods for modelling and measuring the extreme financial risks. We illustrate that the approach based on extreme value theory is very useful for estimating tail related risk measures through backtesting of an empirical data.

• Journal of Korean Neurosurgical Society
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• v.67 no.1
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• pp.60-72
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• 2024

Objective : Recently, robotic-assisted spine surgery (RASS) has been considered a minimally invasive and relatively accurate method. In total, 495 robotic-assisted pedicle screw fixation (RAPSF) procedures were attempted on 100 patients during a 14-month period. The current study aimed to analyze the accuracy, potential risk factors, and learning curve of RAPSF. Methods : This retrospective study evaluated the position of RAPSF using the Gertzbein and Robbins scale (GRS). The accuracy was analyzed using the ratio of the clinically acceptable group (GRS grades A and B), the dissatisfying group (GRS grades C, D, and E), and the Surgical Evaluation Assistant program. The RAPSF was divided into the no-breached group (GRS grade A) and breached group (GRS grades B, C, D, and E), and the potential risk factors of RAPSF were evaluated. The learning curve was analyzed by changes in robot-used time per screw and the occurrence tendency of breached and failed screws according to case accumulation. Results : The clinically acceptable group in RAPSF was 98.12%. In the analysis using the Surgical Evaluation Assistant program, the tip offset was 2.37±1.89 mm, the tail offset was 3.09±1.90 mm, and the angular offset was 3.72°±2.72°. In the analysis of potential risk factors, the difference in screw fixation level (p=0.009) and segmental distance between the tracker and the instrumented level (p=0.001) between the no-breached and breached group were statistically significant, but not for the other factors. The mean difference between the no-breach and breach groups was statistically significant in terms of pedicle width (p<0.001) and tail offset (p=0.042). In the learning curve analysis, the occurrence of breached and failed screws and the robot-used time per screw screws showed a significant decreasing trend. Conclusion : In the current study, RAPSF was highly accurate and the specific potential risk factors were not identified. However, pedicle width was presumed to be related to breached screw. Meanwhile, the robot-used time per screw and the incidence of breached and failed screws decreased with the learning curve.

• Journal of Korean Tunnelling and Underground Space Association
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• v.26 no.4
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• pp.303-314
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• 2024

Recently, the consecutive shield tunnel boring machine (TBM) has gained attention for its potential to enhance TBM penetration rates. However, its development requires a thorough risk assessment due to the unconventional nature of its equipment and hydraulic systems, coupled with the absence of design or construction precedents. This study investigated the causal relationships between four accidents and eight relevant sources associated with the consecutive shield TBM. Subsequently, risk levels were determined based on expert surveys and a risk matrix technique. The findings highlighted significant impacts associated with collapses or surface settlements and the likelihood of causal combinations leading to misalignment. Specifically, this study emphasized the importance of proactive mitigation measures to address collapses or surface settlements caused by inadequate continuous tail void backfill or damaged thrust jacks. Furthermore, it is recommended to develop advanced non-destructive testing technology capable of comprehensive range detection across helical segments, to design a sequential thrust jack propulsion system, and to determine an optimal pedestal angle.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.87-99
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• 2007

In this paper, we consider the Sparre Andersen risk model modified by the inclusion of interest on the surplus. By using the techniques of Cai and Dickson [Ins.: Math. Econ. 32(2003)], we give the functional and also the exponential type upper bounds for the tail probability of the deficit at ruin. Some special cases are also discussed.