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Published: 9 March 2023
Last updated: 10 March 2023

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1

Xun, Li, Renqiao Jiang, and Jianhua Guo. "The conditional Haezendonck–Goovaerts risk measure." Statistics & Probability Letters 169 (February 2021): 108968. http://dx.doi.org/10.1016/j.spl.2020.108968.

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2

Ding, Rui, and Stan Uryasev. "CoCDaR and mCoCDaR: New Approach for Measurement of Systemic Risk Contributions." Journal of Risk and Financial Management 13, no. 11 (November 3, 2020): 270. http://dx.doi.org/10.3390/jrfm13110270.

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Systemic risk is the risk that the distress of one or more institutions trigger a collapse of the entire financial system. We extend CoVaR (value-at-risk conditioned on an institution) and CoCVaR (conditional value-at-risk conditioned on an institution) systemic risk contribution measures and propose a new CoCDaR (conditional drawdown-at-risk conditioned on an institution) measure based on drawdowns. This new measure accounts for consecutive negative returns of a security, while CoVaR and CoCVaR combine together negative returns from different time periods. For instance, ten 2% consecutive losses resulting in 20% drawdown will be noticed by CoCDaR, while CoVaR and CoCVaR are not sensitive to relatively small one period losses. The proposed measure provides insights for systemic risks under extreme stresses related to drawdowns. CoCDaR and its multivariate version, mCoCDaR, estimate an impact on big cumulative losses of the entire financial system caused by an individual firm’s distress. It can be used for ranking individual systemic risk contributions of financial institutions (banks). CoCDaR and mCoCDaR are computed with CVaR regression of drawdowns. Moreover, mCoCDaR can be used to estimate drawdowns of a security as a function of some other factors. For instance, we show how to perform fund drawdown style classification depending on drawdowns of indices. Case study results, data, and codes are posted on the web.
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3

Kuzmina, Jekaterina, Gaida Pettere, and Irina Voronova. "Conditional risk measure modeling for Latvian insurance companies." Perspectives of Innovations, Economics and Business 2, no. 2 (October 9, 2009): 59–61. http://dx.doi.org/10.15208/pieb.2009.56.

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4

Dmitrasinovic-Vidovic, Gordana, Ali Lari-Lavassani, Xun Li, and Antony Ware. "Continuous Time Portfolio Selection under Conditional Capital at Risk." Journal of Probability and Statistics 2010 (2010): 1–26. http://dx.doi.org/10.1155/2010/976371.

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Portfolio optimization with respect to different risk measures is of interest to both practitioners and academics. For there to be a well-defined optimal portfolio, it is important that the risk measure be coherent and quasiconvex with respect to the proportion invested in risky assets. In this paper we investigate one such measure—conditional capital at risk—and find the optimal strategies under this measure, in the Black-Scholes continuous time setting, with time dependent coefficients.
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5

Kim, Joseph H. T., and Mary R. Hardy. "Estimating the Variance of Bootstrapped Risk Measures." ASTIN Bulletin 39, no. 1 (May 2009): 199–223. http://dx.doi.org/10.2143/ast.39.1.2038062.

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AbstractIn Kim and Hardy (2007) the exact bootstrap was used to estimate certain risk measures including Value at Risk and the Conditional Tail Expectation. In this paper we continue this work by deriving the influence function of the exact-bootstrapped quantile risk measure. We can use the influence function to estimate the variance of the exact-bootstrap risk measure. We then extend the result to the L-estimator class, which includes the conditional tail expectation risk measure. The resulting formula provides an alternative way to estimate the variance of the bootstrapped risk measures, or the whole L-estimator class in an analytic form. A simulation study shows that this new method is comparable to the ordinary resampling-based bootstrap method, with the advantages of an analytic approach.
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6

Brownlees, Christian, and Robert F. Engle. "SRISK: A Conditional Capital Shortfall Measure of Systemic Risk." Review of Financial Studies 30, no. 1 (August 6, 2016): 48–79. http://dx.doi.org/10.1093/rfs/hhw060.

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7

MÖLLER, PHILIPP M. "DRAWDOWN MEASURES AND RETURN MOMENTS." International Journal of Theoretical and Applied Finance 21, no. 07 (November 2018): 1850042. http://dx.doi.org/10.1142/s0219024918500425.

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This paper provides an investigation of the effects of an investment’s return moments on drawdown-based measures of risk, including Maximum Drawdown (MDD), Conditional Drawdown (CDD), and Conditional Expected Drawdown (CED). Additionally, a new end-of-period drawdown measure is introduced, which incorporates a psychological aspect of risk perception that previous drawdown measures had been unable to capture. While simulation results indicate many similarities in the first and second moments, skewness and kurtosis affect different drawdown measures in radically different ways. Thus, users should assess whether their choice of drawdown measure accurately reflects the kind of risk they want to measure.
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8

Hürlimann, Werner. "Multivariate Fréchet copulas and conditional value-at-risk." International Journal of Mathematics and Mathematical Sciences 2004, no. 7 (2004): 345–64. http://dx.doi.org/10.1155/s0161171204210158.

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Based on the method of copulas, we construct a parametric family of multivariate distributions using mixtures of independent conditional distributions. The new family of multivariate copulas is a convex combination of products of independent and comonotone subcopulas. It fulfills the four most desirable properties that a multivariate statistical model should satisfy. In particular, the bivariate margins belong to a simple but flexible one-parameter family of bivariate copulas, called linear Spearman copula, which is similar but not identical to the convex family of Fréchet. It is shown that the distribution and stop-loss transform of dependent sums from this multivariate family can be evaluated using explicit integral formulas, and that these dependent sums are bounded in convex order between the corresponding independent and comonotone sums. The model is applied to the evaluation of the economic risk capital for a portfolio of risks using conditional value-at-risk measures. A multivariate conditional value-at-risk vector measure is considered. Its components coincide for the constructed multivariate copula with the conditional value-at-risk measures of the risk components of the portfolio. This yields a “fair” risk allocation in the sense that each risk component becomes allocated to its coherent conditional value-at-risk.
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9

Ghosh, Indranil, and Filipe J. Marques. "Tail Conditional Expectations Based on Kumaraswamy Dispersion Models." Mathematics 9, no. 13 (June 24, 2021): 1478. http://dx.doi.org/10.3390/math9131478.

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Recently, there seems to be an increasing amount of interest in the use of the tail conditional expectation (TCE) as a useful measure of risk associated with a production process, for example, in the measurement of risk associated with stock returns corresponding to the manufacturing industry, such as the production of electric bulbs, investment in housing development, and financial institutions offering loans to small-scale industries. Companies typically face three types of risk (and associated losses from each of these sources): strategic (S); operational (O); and financial (F) (insurance companies additionally face insurance risks) and they come from multiple sources. For asymmetric and bounded losses (properly adjusted as necessary) that are continuous in nature, we conjecture that risk assessment measures via univariate/bivariate Kumaraswamy distribution will be efficient in the sense that the resulting TCE based on bivariate Kumaraswamy type copulas do not depend on the marginals. In fact, almost all classical measures of tail dependence are such, but they investigate the amount of tail dependence along the main diagonal of copulas, which has often little in common with the concentration of extremes in the copula’s domain of definition. In this article, we examined the above risk measure in the case of a univariate and bivariate Kumaraswamy (KW) portfolio risk, and computed TCE based on bivariate KW type copulas. For illustrative purposes, a well-known Stock indices data set was re-analyzed by computing TCE for the bivariate KW type copulas to determine which pairs produce minimum risk in a two-component risk scenario.
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10

Di Bernardino, E., J. M. Fernández-Ponce, F. Palacios-Rodríguez, and M. R. Rodríguez-Griñolo. "On multivariate extensions of the conditional Value-at-Risk measure." Insurance: Mathematics and Economics 61 (March 2015): 1–16. http://dx.doi.org/10.1016/j.insmatheco.2014.11.006.

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11

Banihashemi, Shokoofeh, Ali Azarpour, and Marziye Kaveh. "Multi-stage stochastic model in portfolio selection problem." Filomat 32, no. 3 (2018): 991–1001. http://dx.doi.org/10.2298/fil1803991b.

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This paper is a novel work of portfolio-selection problem solving using multi objective model considering four parameters, Expected return, downside beta coefficient, semivariance and conditional value at risk at a specified confidence level. Multi-period models can be defined as stochastic models. Early studies on portfolio selection developed using variance as a risk measure; although, theories and practices revealed that variance, considering its downsides, is not a desirable risk measure. To increase accuracy and overcoming negative aspects of variance, downside risk measures like semivarinace, downside beta covariance, value at risk and conditional value at risk was other risk measures that replaced in models. These risk measures all have advantages over variance and previous works using these parameters have shown improvements in the best portfolio selection. Purposed models are solved using genetic algorithm and for the topic completion, numerical example and plots to measure the performance of model in four dimensions are provided.
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12

CHEKHLOV, ALEXEI, STANISLAV URYASEV, and MICHAEL ZABARANKIN. "DRAWDOWN MEASURE IN PORTFOLIO OPTIMIZATION." International Journal of Theoretical and Applied Finance 08, no. 01 (January 2005): 13–58. http://dx.doi.org/10.1142/s0219024905002767.

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A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter α, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 - α) * 100% drawdowns. The CDD measure generalizes the notion of the drawdown functional to a multi-scenario case and can be considered as a generalization of deviation measure to a dynamic case. The CDD measure includes the Maximal Drawdown and Average Drawdown as its limiting cases. Mathematical properties of the CDD measure have been studied and efficient optimization techniques for CDD computation and solving asset-allocation problems with a CDD measure have been developed. The CDD family of risk functionals is similar to Conditional Value-at-Risk (CVaR), which is also called Mean Shortfall, Mean Excess Loss, or Tail Value-at-Risk. Some recommendations on how to select the optimal risk functionals for getting practically stable portfolios have been provided. A real-life asset-allocation problem has been solved using the proposed measures. For this particular example, the optimal portfolios for cases of Maximal Drawdown, Average Drawdown, and several intermediate cases between these two have been found.
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13

HIDAYATI, HERLINA, KOMANG DHARMAWAN, and I. WAYAN SUMARJAYA. "ESTIMASI NILAI CONDITIONAL VALUE AT RISK MENGGUNAKAN FUNGSI GAUSSIAN COPULA." E-Jurnal Matematika 4, no. 4 (November 24, 2015): 188. http://dx.doi.org/10.24843/mtk.2015.v04.i04.p110.

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Copula is already widely used in financial assets, especially in risk management. It is due to the ability of copula, to capture the nonlinear dependence structure on multivariate assets. In addition, using copula function doesn’t require the assumption of normal distribution. There fore it is suitable to be applied to financial data. To manage a risk the necessary measurement tools can help mitigate the risks. One measure that can be used to measure risk is Value at Risk (VaR). Although VaR is very popular, it has several weaknesses. To overcome the weakness in VaR, an alternative risk measure called CVaR can be used. The porpose of this study is to estimate CVaR using Gaussian copula. The data we used are the closing price of Facebook and Twitter stocks. The results from the calculation using 90% confidence level showed that the risk that may be experienced is at 4,7%, for 95% confidence level it is at 6,1%, and for 99% confidence level it is at 10,6%.
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14

Pflug, Georg Ch. "Coherent Risk Measures and Convex Combinations of the Conditional Value at Risk (C V@R)." Austrian Journal of Statistics 31, no. 1 (April 3, 2016): 73–75. http://dx.doi.org/10.17713/ajs.v31i1.471.

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The conditional-value-at-risk (C V@R) has been widely used as a risk measure. It is well known, that C V@R is coherent in the sense of Artzner, Delbaen, Eber, Heath (1999). The class of coherent risk measures is convex. It was conjectured, that all coherent risk measures can be represented as convex combinations of C V@R’s. In this note we show that this conjecture is wrong.
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15

Wang, Yu Ling, Jun Hai Ma, and Yu Hua Xu. "Risk Asset Portfolio Choice Models under Three Risk Measures." Advanced Materials Research 204-210 (February 2011): 537–40. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.537.

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Mean-variance model, value at risk and Conditional Value at Risk are three chief methods to measure financial risk recently. The demonstrative research shows that three optional questions are equivalence when the security rates have a multivariate normal distribution and the given confidence level is more than a special value. Applications to real data provide empirical support to this methodology. This result has provided new methods for us about further research of risk portfolios.
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16

Smith, Warwick. "The decision support model for risk management." Bulletin of the New Zealand Society for Earthquake Engineering 37, no. 4 (December 31, 2004): 149–55. http://dx.doi.org/10.5459/bnzsee.37.4.149-155.

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Risk management decisions often demand the allocation of scarce resources in mitigation of different hazards. A quantitative basis for decision-making can be provided by a detailed risk assessment, in which the current risk and those that obtain under proposed projects can be evaluated. The average annual loss, or expected value, is not a useful measure of extreme risk. The conditional expected value, calculated for a series of probability ranges, provides measures of the risk that can be assembled into a decision table so that informed decisions can be made. The conditional expected value can be calculated even when the losses are only available in terms of a cumulative probability function.
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17

Cai, Jun, and Haijun Li. "Conditional tail expectations for multivariate phase-type distributions." Journal of Applied Probability 42, no. 3 (September 2005): 810–25. http://dx.doi.org/10.1239/jap/1127322029.

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The conditional tail expectation in risk analysis describes the expected amount of risk that can be experienced given that a potential risk exceeds a threshold value, and provides an important measure of right-tail risk. In this paper, we study the convolution and extreme values of dependent risks that follow a multivariate phase-type distribution, and derive explicit formulae for several conditional tail expectations of the convolution and extreme values for such dependent risks. Utilizing the underlying Markovian property of these distributions, our method not only provides structural insight, but also yields some new distributional properties of multivariate phase-type distributions.
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18

Cai, Jun, and Haijun Li. "Conditional tail expectations for multivariate phase-type distributions." Journal of Applied Probability 42, no. 03 (September 2005): 810–25. http://dx.doi.org/10.1017/s0021900200000796.

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The conditional tail expectation in risk analysis describes the expected amount of risk that can be experienced given that a potential risk exceeds a threshold value, and provides an important measure of right-tail risk. In this paper, we study the convolution and extreme values of dependent risks that follow a multivariate phase-type distribution, and derive explicit formulae for several conditional tail expectations of the convolution and extreme values for such dependent risks. Utilizing the underlying Markovian property of these distributions, our method not only provides structural insight, but also yields some new distributional properties of multivariate phase-type distributions.
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19

Tabasi, Hamed, Vahidreza Yousefi, Jolanta Tamošaitienė, and Foroogh Ghasemi. "Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models." Administrative Sciences 9, no. 2 (May 24, 2019): 40. http://dx.doi.org/10.3390/admsci9020040.

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This paper attempted to calculate the market risk in the Tehran Stock Exchange by estimating the Conditional Value at Risk. Since the Conditional Value at Risk is a tail-related measure, Extreme Value Theory has been utilized to estimate the risk more accurately. Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models were used to model the volatility-clustering feature, and to estimate the parameters of the model, the Maximum Likelihood method was applied. The results of the study showed that in the estimation of model parameters, assuming T-student distribution function gave better results than the Normal distribution function. The Monte Carlo simulation method was used for backtesting the Conditional Value at Risk model, and in the end, the performance of different models, in the estimation of this measure, was compared.
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20

Bosch-Badia, Maria-Teresa, Joan Montllor-Serrats, and Maria-Antonia Tarrazon-Rodon. "Risk Analysis through the Half-Normal Distribution." Mathematics 8, no. 11 (November 21, 2020): 2080. http://dx.doi.org/10.3390/math8112080.

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We study the applicability of the half-normal distribution to the probability–severity risk analysis traditionally performed through risk matrices and continuous probability–consequence diagrams (CPCDs). To this end, we develop a model that adapts the financial risk measures Value-at-Risk (VaR) and Conditional Value at Risk (CVaR) to risky scenarios that face only negative impacts. This model leads to three risk indicators: The Hazards Index-at-Risk (HIaR), the Expected Hazards Damage (EHD), and the Conditional HIaR (CHIaR). HIaR measures the expected highest hazards impact under a certain probability, while EHD consists of the expected impact that stems from truncating the half-normal distribution at the HIaR point. CHIaR, in turn, measures the expected damage in the case it exceeds the HIaR. Therefore, the Truncated Risk Model that we develop generates a measure for hazards expectations (EHD) and another measure for hazards surprises (CHIaR). Our analysis includes deduction of the mathematical functions that relate HIaR, EHD, and CHIaR to one another as well as the expected loss estimated by risk matrices. By extending the model to the generalised half-normal distribution, we incorporate a shape parameter into the model that can be interpreted as a hazard aversion coefficient.
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21

Landsman, Zinoviy, and Emiliano A. Valdez. "Tail Conditional Expectations for Exponential Dispersion Models." ASTIN Bulletin 35, no. 01 (May 2005): 189–209. http://dx.doi.org/10.2143/ast.35.1.583172.

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There is a growing interest in the use of the tail conditional expectation as a measure of risk. For an institution faced with a random loss, the tail conditional expectation represents the conditional average amount of loss that can be incurred in a fixed period, given that the loss exceeds a specified value. This value is typically based on the quantile of the loss distribution, the so-called value-at-risk. The tail conditional expectation can therefore provide a measure of the amount of capital needed due to exposure to loss. This paper examines this risk measure for “exponential dispersion models”, a wide and popular class of distributions to actuaries which, on one hand, generalizes the Normal and shares some of its many important properties, but on the other hand, contains many distributions of nonnegative random variables like the Gamma and the Inverse Gaussian.
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22

Landsman, Zinoviy, and Emiliano A. Valdez. "Tail Conditional Expectations for Exponential Dispersion Models." ASTIN Bulletin 35, no. 1 (May 2005): 189–209. http://dx.doi.org/10.1017/s0515036100014124.

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There is a growing interest in the use of the tail conditional expectation as a measure of risk. For an institution faced with a random loss, the tail conditional expectation represents the conditional average amount of loss that can be incurred in a fixed period, given that the loss exceeds a specified value. This value is typically based on the quantile of the loss distribution, the so-called value-at-risk. The tail conditional expectation can therefore provide a measure of the amount of capital needed due to exposure to loss. This paper examines this risk measure for “exponential dispersion models”, a wide and popular class of distributions to actuaries which, on one hand, generalizes the Normal and shares some of its many important properties, but on the other hand, contains many distributions of nonnegative random variables like the Gamma and the Inverse Gaussian.
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23

Mwamba, John Weirstrass Muteba, and Serge Angaman. "Systemic risk and real economic activity: A South African insurance stress index of systemic risk." Asian Academy of Management Journal of Accounting and Finance 18, no. 1 (July 29, 2022): 195–218. http://dx.doi.org/10.21315/aamjaf2022.18.1.8.

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This study investigates the link between systemic risk in the South African insurance sector real economic activity in South Africa. To this end, we use six systemic risk measures, the Conditional Value at Risk (CoVaR), the Marginal Conditional Value at Risk (ΔCoVaR), the Comovement and Interconnectedness of the South African insurance sector (Eigen), the Dynamic Mixture Copula Marginal Expected Shortfall (DMC-MES), the Average Conditional Volatility (Ave-vol), and the South African Volatility Index (SAVI). We first evaluate the significance of each measure by assessing its ability to forecast future economic downturns in South Africa. We find that only two systemic risk measures possess the ability to predict future economic downturns in South Africa. We then use principal component quantile regression analysis to aggregate these measures into a composite stress index of systemic risk for the South African insurance sector and assess the ability of the proposed index to predict future economic downturns in South Africa. Our results reveal that the proposed index is a good predictor of future economic downturns in South Africa. Thus, our results suggest that regulators and risk managers must develop an analysis of systemic risk in the insurance sector with particular attention to its effects on real economic activity. In addition, our index can potentially be used as an instrument to monitor and mitigate systemic risk in the insurance sector in order to ensure the stability of the financial system and the economy in South Africa.
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24

Ghorbel, Ahmed, and Abdelwahed Trabelsi. "Measure of financial risk using conditional extreme value copulas with EVT margins." Journal of Risk 11, no. 4 (June 2009): 51–85. http://dx.doi.org/10.21314/jor.2009.196.

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25

Misankova, Maria, and Erika Spuchlakova. "Application of conditional value at risk for credit risk optimization." New Trends and Issues Proceedings on Humanities and Social Sciences 3, no. 4 (March 22, 2017): 146–52. http://dx.doi.org/10.18844/prosoc.v3i4.1540.

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The article is dedicated to the optimization of credit risk through the application of Conditional Value at Risk (CVaR). CVaR is a risk measure, the expected loss exceeding Value-at-Risk and is also known as Mean Excess, Mean Shortfall, or Tail VaR. The link between credit risk and the current financial crisis accentuates the importance of measuring and predicting extreme credit risk. Conditional Value at Risk has become an increasingly popular method for measurement and optimization of extreme market risk. The use of model can regulate all positions in a portfolio of financial instruments in order to minimize CVaR subject to trading and return constraints at the same time. The credit risk distribution is created by Monte Carlo simulations and the optimization problem is solved effectively by linear programming. We apply these CVaR techniques to the optimization of credit risk on portfolio of selected bonds.                  Keywords: value at risk; conditional value at risk; credit risk; portfolio
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26

Sawik, Bartosz. "A Bi-Objective Portfolio Optimization with Conditional Value-at-Risk." Decision Making in Manufacturing and Services 4, no. 2 (December 19, 2010): 47–69. http://dx.doi.org/10.7494/dmms.2010.4.2.47.

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This paper presents a bi-objective portfolio model with the expected return as a performance measure and the expected worst-case return as a risk measure. The problems are formulated as a bi-objective linear program. Numerical examples based on 1000, 3500 and 4020 historical daily input data from the Warsaw Stock Exchange are presented and selected computational results are provided. The computational experiments prove that the proposed linear programming approach provides the decision maker with a simple tool for evaluating the relationship between the expected and the worst-case portfolio return.
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Koike, Takaaki, and Marius Hofert. "Markov Chain Monte Carlo Methods for Estimating Systemic Risk Allocations." Risks 8, no. 1 (January 15, 2020): 6. http://dx.doi.org/10.3390/risks8010006.

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In this paper, we propose a novel framework for estimating systemic risk measures and risk allocations based on Markov Chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By considering a crisis event as an intersection of linear constraints, this class of allocations covers, for example, conditional Value-at-Risk (CoVaR), conditional expected shortfall (CoES), VaR contributions, and range VaR (RVaR) contributions as special cases. For this class of allocations, analytical calculations are rarely available, and numerical computations based on Monte Carlo (MC) methods often provide inefficient estimates due to the rare-event character of the crisis events. We propose an MCMC estimator constructed from a sample path of a Markov chain whose stationary distribution is the conditional distribution given the crisis event. Efficient constructions of Markov chains, such as the Hamiltonian Monte Carlo and Gibbs sampler, are suggested and studied depending on the crisis event and the underlying loss distribution. The efficiency of the MCMC estimators is demonstrated in a series of numerical experiments.
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28

Hamad, Amneh, Mohammad AL-Momani, and Hamzah Al-Mawali. "Does Accounting Conservatism Mitigate the Operating Cash Flows Downside Risk?" Journal of Social Sciences Research, no. 52 (January 25, 2019): 472–83. http://dx.doi.org/10.32861/jssr.52.472.483.

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The aim of this study is to investigate whether the two types of accounting conservatism (conditional and unconditional) mitigate the risk of falling operating cash flows in the presence of cash holdings of Jordanian companies for the period from (2005–2014) for a sample of (160) companies listed in Amman Stock Exchange (ASE). By using the principle components analysis method in the SPSS system to generate a composite measure for the measurement of the conditional conservatism (CC_CM) consisting of three measures: negative accruals (CC_NACC), current accruals to total accruals (CC_CACC), and accounting conservatism to the good news (CC_ACGN). As well as to generate another composite measure for the measurement of the unconditional conservatism (UC_CM) consisting of three measures: total accrual (UC_TACC), book to market (UC_BTM) ratio, and skewness (UC_Skew). In order to measure the downside risk of operating cash flows, we used the root lower partial moment of operating cash flow (RLPM_OCF). We find that two types of accounting conservatism are significantly positively effect on cash holdings. In addition, we conclude that there is a significantly negatively indirect effect for accounting conservatism on downside risk of operating cash flows in Jordanian companies that have cash holdings. It means that the increasing of the accounting conservatism leads to the increasing of cash holdings, which leads to mitigate the operating cash flows downside risk.
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29

Takada, Hellinton H., Sylvio X. Azevedo, Julio M. Stern, and Celma O. Ribeiro. "Using Entropy to Forecast Bitcoin’s Daily Conditional Value at Risk." Proceedings 33, no. 1 (November 21, 2019): 7. http://dx.doi.org/10.3390/proceedings2019033007.

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Conditional value at risk (CVaR), or expected shortfall, is a risk measure for investments according to Rockafellar and Uryasev. Yamai and Yoshiba define CVaR as the conditional expectation of loss given that the loss is beyond the value at risk (VaR) level. The VaR is a risk measure that represents how much an investment might lose during usual market conditions with a given probability in a time interval. In particular, Rockafellar and Uryasev show that CVaR is superior to VaR in applications related to investment portfolio optimization. On the other hand, the Shannon entropy has been used as an uncertainty measure in investments and, in particular, to forecast the Bitcoin’s daily VaR. In this paper, we estimate the entropy of intraday distribution of Bitcoin’s logreturns through the symbolic time series analysis (STSA) and we forecast Bitcoin’s daily CVaR using the estimated entropy. We find that the entropy is positively correlated to the likelihood of extreme values of Bitcoin’s daily logreturns using a logistic regression model based on CVaR and the use of entropy to forecast the Bitcoin’s daily CVaR of the next day performs better than the naive use of the historical CVaR.
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30

Jiang, Daniel R., and Warren B. Powell. "Risk-Averse Approximate Dynamic Programming with Quantile-Based Risk Measures." Mathematics of Operations Research 43, no. 2 (May 2018): 554–79. http://dx.doi.org/10.1287/moor.2017.0872.

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In this paper, we consider a finite-horizon Markov decision process (MDP) for which the objective at each stage is to minimize a quantile-based risk measure (QBRM) of the sequence of future costs; we call the overall objective a dynamic quantile-based risk measure (DQBRM). In particular, we consider optimizing dynamic risk measures where the one-step risk measures are QBRMs, a class of risk measures that includes the popular value at risk (VaR) and the conditional value at risk (CVaR). Although there is considerable theoretical development of risk-averse MDPs in the literature, the computational challenges have not been explored as thoroughly. We propose data-driven and simulation-based approximate dynamic programming (ADP) algorithms to solve the risk-averse sequential decision problem. We address the issue of inefficient sampling for risk applications in simulated settings and present a procedure, based on importance sampling, to direct samples toward the “risky region” as the ADP algorithm progresses. Finally, we show numerical results of our algorithms in the context of an application involving risk-averse bidding for energy storage. The online appendix is available at https://doi.org/10.1287/moor.2017.0872 .
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Landsman, Zinoviy, and Tomer Shushi. "Multivariate Tail Moments for Log-Elliptical Dependence Structures as Measures of Risks." Symmetry 13, no. 4 (March 28, 2021): 559. http://dx.doi.org/10.3390/sym13040559.

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The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.
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32

Dixit, Vijaya, and Manoj Kumar Tiwari. "Project portfolio selection and scheduling optimization based on risk measure: a conditional value at risk approach." Annals of Operations Research 285, no. 1-2 (April 6, 2019): 9–33. http://dx.doi.org/10.1007/s10479-019-03214-1.

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33

Long, H. Viet, H. Bin Jebreen, I. Dassios, and D. Baleanu. "On the Statistical GARCH Model for Managing the Risk by Employing a Fat-Tailed Distribution in Finance." Symmetry 12, no. 10 (October 15, 2020): 1698. http://dx.doi.org/10.3390/sym12101698.

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The Conditional Value-at-Risk (CVaR) is a coherent measure that evaluates the risk for different investing scenarios. On the other hand, since the extreme value distribution has been revealed to furnish better financial and economical data adjustment in contrast to the well-known normal distribution, we here employ this distribution in investigating explicit formulas for the two common risk measures, i.e., VaR and CVaR, to have better tools in risk management. The formulas are then employed under the generalized autoregressive conditional heteroskedasticity (GARCH) model for risk management as our main contribution. To confirm the theoretical discussions of this work, the daily returns of several stocks are considered and worked out. The simulation results uphold the superiority of our findings.
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34

Fuchs, Sebastian, and Wolfgang Trutschnig. "On quantile based co-risk measures and their estimation." Dependence Modeling 8, no. 1 (December 21, 2020): 396–416. http://dx.doi.org/10.1515/demo-2020-0021.

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AbstractConditional Value-at-Risk (CoVaR) is defined as the Value-at-Risk of a certain risk given that the related risk equals a given threshold (CoVaR=) or is smaller/larger than a given threshold (CoVaR</CoVaR≥). We extend the notion of Conditional Value-at-Risk to quantile based co-risk measures that are weighted mixtures of CoVaR at different levels and hence involve the stochastic dependence that occurs among the risks and that is captured by copulas. We show that every quantile based co-risk measure is a quantile based risk measure and hence fulfills all related properties. We further discuss continuity results of quantile based co-risk measures from which consistent estimators for CoVaR< and CoVaR≥ based risk measures immediately follow when plugging in empirical copulas. Although estimating co-risk measures based on CoVaR= is a nontrivial endeavour since conditioning on events with zero probability is necessary we show that working with so-called empirical checkerboard copulas allows to construct strongly consistent estimators for CoVaR= and related co-risk measures under very mild regularity conditions. A small simulation study illustrates the performance of the obtained estimators for special classes of copulas.
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35

Indarwati, Ervin, and Rosita Kusumawati. "Estimation of the Portfolio Risk from Conditional Value at Risk Using Monte Carlo Simulation." Jurnal Matematika, Statistika dan Komputasi 17, no. 3 (May 12, 2021): 370–80. http://dx.doi.org/10.20956/j.v17i3.11340.

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Portfolio risk shows the large deviations in portfolio returns from expected portfolio returns. Value at Risk (VaR) is one method for determining the maximum risk of loss of a portfolio or an asset based on a certain probability and time. There are three methods to estimate VaR, namely variance-covariance, historical, and Monte Carlo simulations. One disadvantage of VaR is that it is incoherent because it does not have sub-additive properties. Conditional Value at Risk (CVaR) is a coherent or related risk measure and has a sub-additive nature which indicates that the loss on the portfolio is smaller or equal to the amount of loss of each asset. CVaR can provide loss information above the maximum loss. Estimating portfolio risk from the CVaR value using Monte Carlo simulation and its application to PT. Bank Negara Indonesia (Persero) Tbk (BBNI.JK) and PT. Bank Tabungan Negara (Persero) Tbk (BBTN.JK) will be discussed in this study. The daily closing price of each BBNI and BBTN share from 6 January 2019 to 30 December 2019 is used to measure the CVaR of the two banks' stock portfolios with this Monte Carlo simulation. The steps taken are determining the return value of assets, testing the normality of return of assets, looking for risk measures of returning assets that form a normally distributed portfolio, simulate the return of assets with monte carlo, calculate portfolio weights, looking for returns portfolio, calculate the quartile of portfolio return as a VaR value, and calculate the average loss above the VaR value as a CVaR value. The results of portfolio risk estimation of the value of CVaR using Monte Carlo simulation on PT. Bank Negara Indonesia (Persero) Tbk and PT. Bank Tabungan Negara (Persero) Tbk at a confidence level of 90%, 95%, and 99% is 5.82%, 6.39%, and 7.1% with a standard error of 0.58%, 0.59%, and 0.59%. If the initial funds that will be invested in this portfolio are illustrated at Rp 100,000,000, it can be interpreted that the maximum possible risk that investors will receive in the future will not exceed Rp 5,820,000, Rp 6,390,000 and Rp 7,100,000 at the significant level 90%, 95%, and 99%
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36

Wackowski, Olivia A., and Michelle Jeong. "Comparison of a General and Conditional Measure of E-Cigarette Harm Perceptions." International Journal of Environmental Research and Public Health 17, no. 14 (July 17, 2020): 5151. http://dx.doi.org/10.3390/ijerph17145151.

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Measures of tobacco product harm perceptions are important in research, given their association with tobacco use. Despite recommendations to use more specific harm and risk perception measures, limited research exists comparing different wordings. We present exploratory survey data comparing young adults’ (ages 18–29) responses to a general e-cigarette harm perception measure (“How harmful, if at all, do you think vaping/using an e-cigarette is to a user’s health?”) with a more specific conditional measure, which personalized the behavior/harm (“imagine you vaped,” “your health”) and presented a specific use condition (exclusive daily vaping) and timeframe (10 years). Data were collected in January 2019 (n = 1006). Measures were highly correlated (r = 0.76, Cronbach’s α = 0.86), and most (65%) provided consistent responses, although more participants rated e-cigarettes as very or extremely harmful using the conditional (51.6%) versus the general (43.9%) harm measure. However, significant differences in harm ratings were not observed among young adults who currently vaped. Correlations between each harm perception measure and measures of e-cigarette use intentions were similar. More specifically worded harm perception measures may result in somewhat higher e-cigarette harm ratings than general measures for some young adults. Additional research on best practices for measuring e-cigarette and other tobacco harm perceptions is warranted.
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37

Bollen, Nicolas P. B., and Veronika K. Pool. "Conditional Return Smoothing in the Hedge Fund Industry." Journal of Financial and Quantitative Analysis 43, no. 2 (June 2008): 267–98. http://dx.doi.org/10.1017/s0022109000003525.

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AbstractWe show that if true returns are independently distributed and a manager fully reports gains but delays reporting losses, then reported returns will feature conditional serial correlation. We use conditional serial correlation as a measure of conditional return smoothing. We estimate conditional serial correlation in a large sample of hedge funds. We find that the probability of observing conditional serial correlation is related to the volatility and magnitude of investor cash flows, consistent with conditional return smoothing in response to the risk of capital flight. We also present evidence that conditional serial correlation is a leading indicator of fraud.
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38

Fawzi, M. T., O. Hakim, and H. Nacera. "CONFIDENCE INTERVALS OF THE ADJUSTED TAIL CONDITIONAL EXPECTATION RISK MEASURE FOR A STATIONARY SERIE." Advances in Mathematics: Scientific Journal 10, no. 11 (November 22, 2021): 3395–408. http://dx.doi.org/10.37418/amsj.10.11.3.

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In this paper we present a semi-parametric estimator of the adjusted tail conditional expectation risk measure based on the theory of extreme values for a stationary serie. We prove its asymptotic normality and we construct the confidence intervals. The accuracy of these intervals is evaluated through a simulation study.
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39

Chen, Xiu Fang, and Gao Bo Chen. "Pattern Search for Generalized Hyperbolic Distribution and Financial Risk Measure." Applied Mechanics and Materials 155-156 (February 2012): 424–29. http://dx.doi.org/10.4028/www.scientific.net/amm.155-156.424.

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A new parameter estimation--- pattern search algorithm based on maximum likelihood estimation is used to estimate the parameters of generalized hyperbolic distribution, normal inverse Gaussian distribution and hyperbolic distribution, which are used to fit the log-return of Shanghai composite index. The goodness of fit is tested based on Anderson & Darling distance and FOF distance who pay more attention to tail distances of some distribution. Monte Carlo simulation are used to determin the critical values of Anderson & Darling distance and FOF distance of different distributions.Value at risk (VaR) and conditional value at risk (CVaR) are estimated for the fitted generalized hyperbolic distribution, normal inverse Gaussian distribution and hyperbolic distributio.The results show that generalized hyperbolic distribution family is more suitable for risk measure such as VaR and CVaR than normal distribution.
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40

Nahar, Vinayak K., Michael A. Vice, and M. Allison Ford. "Conceptualizing and Measuring Risk Perceptions of Skin Cancer." Californian Journal of Health Promotion 11, no. 3 (December 1, 2013): 36–47. http://dx.doi.org/10.32398/cjhp.v11i3.1540.

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Background: Perceived risk is commonly conceived as a joint function of the perceived evaluations about the probability estimate of a negative outcome, and the perceived seriousness of the consequences of that negative outcome. Theories typically posit that once people perceive their vulnerability to health risks or outcomes, they form intentions to take preventive actions to reduce their risk. This theoretical proposition is not supported in skin cancer preventative behavior studies, which could be due to improper measurement of perceived risk. Purpose and Methods: The purpose of this manuscript was to assess how risk perception of skin cancer has been conceptualized and measured in the literature to date. Literature retrieval was facilitated through EBSCO, PubMed, PsycInfo, MEDLINE, and ERIC databases. Twenty potentially relevant articles were identified for this review. Results: In the literature, skin cancer risk has been operationalized in two ways: absolute risk and comparative risk. However, these measures have some serious limitations. For example, there is great uncertainty regarding the quality of risk perception measurements (i.e., whether the items used to measure perceived risk are reliable and valid). Future studies are warranted to better understand the significance of using conditional risk measures.
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41

Walls, W. D., and Wei Zhang. "Using Extreme Value Theory to Model Electricity Price Risk with an Application to the Alberta Power Market." Energy Exploration & Exploitation 23, no. 5 (October 2005): 375–403. http://dx.doi.org/10.1260/014459805775992690.

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Value-at-risk (VaR) is a measure of the maximum potential change in value of a portfolio of financial assets with a given probability over a given time horizon. VaR has become a standard measure of market risk and a common practice is to compute VaR by assuming that changes in value of the portfolio are conditionally normally distributed. However, assets returns usually come from heavy-tailed distributions, so computing VaR under the assumption of conditional normality can be an important source of error. We illustrate in our application to competitive electric power prices in Alberta, Canada, that VaR estimates based on extreme value theory models, in particular the generalized Pareto distribution are, more accurate than those produced by alternative models such as normality or historical simulation.
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42

Mendes, Beatriz Vaz de Melo. "Calculando VaR Condicionais Usando Cópulas que Variam no Tempo." Brazilian Review of Finance 3, no. 2 (January 1, 2005): 251. http://dx.doi.org/10.12660/rbfin.v3n2.2005.1152.

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It is now widespread the use of Value-at-Risk (VaR) as a canonical measure at risk. Most accurate VaR measures make use of some volatility model such as GARCH-type models. However, the pattern of volatility dynamic of a portfolio follows from the (univariate) behavior of the risk assets, as well as from the type and strength of the associations among them. Moreover, the dependence structure among the components may change conditionally t past observations. Some papers have attempted to model this characteristic by assuming a multivariate GARCH model, or by considering the conditional correlation coefficient, or by incorporating some possibility for switches in regimes. In this paper we address this problem using time-varying copulas. Our modeling strategy allows for the margins to follow some FIGARCH type model while the copula dependence structure changes over time.
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43

Doria, Serena. "Coherent conditional measures of risk defined by the Choquet integral with respect to Hausdorff outer measure and stochastic independence in risk management." International Journal of Approximate Reasoning 65 (October 2015): 1–10. http://dx.doi.org/10.1016/j.ijar.2015.07.005.

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44

Bäuerle, Nicole, and Tomer Shushi. "Risk management with Tail Quasi-Linear Means." Annals of Actuarial Science 14, no. 1 (October 17, 2019): 170–87. http://dx.doi.org/10.1017/s1748499519000113.

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AbstractWe generalise Quasi-Linear Means by restricting to the tail of the risk distribution and show that this can be a useful quantity in risk management since it comprises in its general form the Value at Risk, the Conditional Tail Expectation and the Entropic Risk Measure in a unified way. We then investigate the fundamental properties of the proposed measure and show its unique features and implications in the risk measurement process. Furthermore, we derive formulas for truncated elliptical models of losses and provide formulas for selected members of such models.
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45

CLÉMENÇON, STÉPHAN, and SKANDER SLIM. "ON PORTFOLIO SELECTION UNDER EXTREME RISK MEASURE: THE HEAVY-TAILED ICA MODEL." International Journal of Theoretical and Applied Finance 10, no. 03 (May 2007): 449–74. http://dx.doi.org/10.1142/s0219024907004275.

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This paper is devoted to the application of the Independent Component Analysis (ICA) methodology to the problem of selecting portfolio strategies, so as to provide against extremal movements in financial markets. A specific ICA model for describing the extreme fluctuations of asset prices is introduced, stipulating that the distributions of the ICs are heavy tailed (i.e., with power law behavior at infinity). An inference method based on conditional maximum likelihood estimation is proposed for our model, which permits to determine practically optimal investment strategies with respect to extreme risk. Empirical studies based on this modeling are carried out to illustrate our approach.
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46

Takeda, Akiko, and Takafumi Kanamori. "A robust approach based on conditional value-at-risk measure to statistical learning problems." European Journal of Operational Research 198, no. 1 (October 2009): 287–96. http://dx.doi.org/10.1016/j.ejor.2008.07.027.

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47

James, Christopher, and Atay Kizilaslan. "Asset Specificity, Industry-Driven Recovery Risk, and Loan Pricing." Journal of Financial and Quantitative Analysis 49, no. 3 (March 13, 2014): 599–631. http://dx.doi.org/10.1017/s0022109014000143.

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AbstractThis paper examines the relationship between a firm’s exposure to industry downturns that we call industry risk and bank loan pricing. We measure industry risk based on the relationship between a firm’s stock returns and industry returns conditional on an industry downturn. We find industry risk is significantly related to the recovery rates in bankruptcy and the likelihood of the firm experiencing financial distress when its peers are also in distress. More importantly, we find that the spreads on unsecured bank loans are positively related to industry risk measures. These relationships are stronger for firms with more industry-specific assets.
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48

Takeda, Akiko, Shuhei Fujiwara, and Takafumi Kanamori. "Extended Robust Support Vector Machine Based on Financial Risk Minimization." Neural Computation 26, no. 11 (November 2014): 2541–69. http://dx.doi.org/10.1162/neco_a_00647.

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Financial risk measures have been used recently in machine learning. For example, [Formula: see text]-support vector machine ([Formula: see text]-SVM) minimizes the conditional value at risk (CVaR) of margin distribution. The measure is popular in finance because of the subadditivity property, but it is very sensitive to a few outliers in the tail of the distribution. We propose a new classification method, extended robust SVM (ER-SVM), which minimizes an intermediate risk measure between the CVaR and value at risk (VaR) by expecting that the resulting model becomes less sensitive than [Formula: see text]-SVM to outliers. We can regard ER-SVM as an extension of robust SVM, which uses a truncated hinge loss. Numerical experiments imply the ER-SVM’s possibility of achieving a better prediction performance with proper parameter setting.
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49

Zhang, Wenjun, and Jin E. Zhang. "GARCH Option Pricing Models and the Variance Risk Premium." Journal of Risk and Financial Management 13, no. 3 (March 9, 2020): 51. http://dx.doi.org/10.3390/jrfm13030051.

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In this paper, we modify Duan’s (1995) local risk-neutral valuation relationship (mLRNVR) for the GARCH option-pricing models. In our mLRNVR, the conditional variances under two measures are designed to be different and the variance process is more persistent in the risk-neutral measure than in the physical one, so that one is able to capture the variance risk premium. Empirical estimation exercises show that the GARCH option-pricing models under our mLRNVR are able to price the SPX one-month variance swap rate, i.e., the CBOE Volatility Index (VIX) accurately. Our research suggests that one should use our mLRNVR when pricing options with GARCH models.
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50

Gajek, Lesław, and Marcin Rudź. "Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model." Methodology and Computing in Applied Probability 22, no. 4 (April 2, 2020): 1507–28. http://dx.doi.org/10.1007/s11009-020-09780-3.

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AbstractInsolvency risk measures play important role in the theory and practice of risk management. In this paper, we provide a numerical procedure to compute vectors of their exact values and prove for them new upper and/or lower bounds which are shown to be attainable. More precisely, we investigate a general insolvency risk measure for a regime-switching Sparre Andersen model in which the distributions of claims and/or wait times are driven by a Markov chain. The measure is defined as an arbitrary increasing function of the conditional expected harm of the deficit at ruin, given the initial state of the Markov chain. A vector-valued operator L, generated by the regime-switching process, is introduced and investigated. We show a close connection between the iterations of L and the risk measure in a finite horizon. The approach assumed in the paper enables to treat in a unified way several discrete and continuous time risk models as well as a variety of important vector-valued insolvency risk measures.
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