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Journal articles on the topic 'Stochastic dominance, VaR, CVaR'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Hürlimann, Werner. "Analytical Bounds for two Value-at-Risk Functionals." ASTIN Bulletin 32, no. 2 (November 2002): 235–65. http://dx.doi.org/10.2143/ast.32.2.1028.

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AbstractBased on the notions of value-at-risk and conditional value-at-risk, we consider two functionals, abbreviated VaR and CVaR, which represent the economic risk capital required to operate a risky business over some time period when only a small probability of loss is tolerated. These functionals are consistent with the risk preferences of profit-seeking (and risk averse) decision makers and preserve the stochastic dominance order (and the stop-loss order). This result is used to bound the VaR and CVaR functionals by determining their maximal values over the set of all loss and profit functions with fixed first few moments. The evaluation of CVaR for the aggregate loss of portfolios is also discussed. The results of VaR and CVaR calculations are illustrated and compared at some typical situations of general interest.

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2

HAN, CHUAN-HSIANG, WEI-HAN LIU, and TZU-YING CHEN. "VaR/CVaR ESTIMATION UNDER STOCHASTIC VOLATILITY MODELS." International Journal of Theoretical and Applied Finance 17, no. 02 (March 2014): 1450009. http://dx.doi.org/10.1142/s0219024914500095.

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This paper proposes an improved procedure for stochastic volatility model estimation with an application to Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) estimation. This improved procedure is composed of the following instrumental components: Fourier transform method for volatility estimation, and importance sampling for extreme event probability estimation. The empirical analysis is based on several foreign exchange series and the S&P 500 index data. In comparison with empirical results by RiskMetrics, historical simulation, and the GARCH(1,1) model, our improved procedure outperforms on average.

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3

Chen, Xi, and Kyoung-Kuk Kim. "Efficient VaR and CVaR Measurement via Stochastic Kriging." INFORMS Journal on Computing 28, no. 4 (November 2016): 629–44. http://dx.doi.org/10.1287/ijoc.2016.0705.

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4

Matousek, Radomil, Pavel Popela, and Jakub Kudela. "Heuristic Approaches to Stochastic Quadratic Assignment Problem: VaR and CVar Cases." MENDEL 23, no. 1 (June 1, 2017): 73–78. http://dx.doi.org/10.13164/mendel.2017.1.073.

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The goal of this paper is to continue our investigation of the heuristic approaches of solving thestochastic quadratic assignment problem (StoQAP) and provide additional insight into the behavior of di erentformulations that arise through the stochastic nature of the problem. The deterministic Quadratic AssignmentProblem (QAP) belongs to a class of well-known hard combinatorial optimization problems. Working with severalreal-world applications we have found that their QAP parameters can (and should) be considered as stochasticones. Thus, we review the StoQAP as a stochastic program and discuss its suitable deterministic reformulations.The two formulations we are going to investigate include two of the most used risk measures - Value at Risk(VaR) and Conditional Value at Risk (CVaR). The focus is on VaR and CVaR formulations and results of testcomputations for various instances of StoQAP solved by a genetic algorithm, which are presented and discussed.

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5

Roveto, Matt, Robert Mieth, and Yury Dvorkin. "Co-Optimization of VaR and CVaR for Data-Driven Stochastic Demand Response Auction." IEEE Control Systems Letters 4, no. 4 (October 2020): 940–45. http://dx.doi.org/10.1109/lcsys.2020.2997259.

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6

Assellaou, Hanane, Brahim Ouhbi, and Bouchra Frikh. "Multi-Objective Programming for Supplier Selection and Order Allocation Under Disruption Risk and Demand, Quality, and Delay Time Uncertainties." International Journal of Business Analytics 5, no. 2 (April 2018): 30–56. http://dx.doi.org/10.4018/ijban.2018040103.

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The purpose of this article is to develop a new stochastic multi objective optimization model to mitigate disruption risks while simultaneously addressing operational risks as well. Indeed, this model considers five objective functions for selecting a set of suppliers considering disruption risk and stochastic demand, quality, and delay time. The authors use two types of risk evaluation models: value-at-risk (VaR) and conditional value-at-risk (CVaR). Two examples are given to illustrate our model and two solution methods are compared and tested.

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7

Ma, Chenghu, and Wing-Keung Wong. "Stochastic dominance and risk measure: A decision-theoretic foundation for VaR and C-VaR." European Journal of Operational Research 207, no. 2 (December 2010): 927–35. http://dx.doi.org/10.1016/j.ejor.2010.05.043.

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8

Chang, Chia-Lin, Juan-Angel Jimenez-Martin, Esfandiar Maasoumi, Michael McAleer, and Teodosio Pérez-Amaral. "Choosing expected shortfall over VaR in Basel III using stochastic dominance." International Review of Economics & Finance 60 (March 2019): 95–113. http://dx.doi.org/10.1016/j.iref.2018.12.016.

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9

Chen, Liyuan, Paola Zerilli, and Christopher F. Baum. "Leverage effects and stochastic volatility in spot oil returns: A Bayesian approach with VaR and CVaR applications." Energy Economics 79 (March 2019): 111–29. http://dx.doi.org/10.1016/j.eneco.2018.03.032.

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10

Angarita-Márquez, Jorge Luis, Geev Mokryani, and Jorge Martínez-Crespo. "Two-Stage Stochastic Model to Invest in Distributed Generation Considering the Long-Term Uncertainties." Energies 14, no. 18 (September 10, 2021): 5694. http://dx.doi.org/10.3390/en14185694.

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This paper used different risk management indicators applied to the investment optimization performed by consumers in Distributed Generation (DG). The objective function is the total cost incurred by the consumer including the energy and capacity payments, the savings, and the revenues from the installation of DG, alongside the operation and maintenance (O&M) and investment costs. Probability density function (PDF) was used to model the price volatility in the long-term. The mathematical model uses a two-stage stochastic approach: investment and operational stages. The investment decisions are included in the first stage and which do not change with the scenarios of the uncertainty. The operation variables are in the second stage and, therefore, take different values with every realization. Three risk indicators were used to assess the uncertainty risk: Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), and Expected Value (EV). The results showed the importance of migration from deterministic models to stochastic ones and, most importantly, the understanding of the ramifications of every risk indicator.

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11

Bourgey, Florian, Stefano De Marco, Emmanuel Gobet, and Alexandre Zhou. "Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations." Monte Carlo Methods and Applications 26, no. 2 (June 1, 2020): 131–61. http://dx.doi.org/10.1515/mcma-2020-2062.

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AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

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12

Nganje, William E., Linda D. Burbidge, Elisha K. Denkyirah, and Elvis M. Ndembe. "Predicting Food-Safety Risk and Determining Cost-Effective Risk-Reduction Strategies." Journal of Risk and Financial Management 14, no. 9 (September 1, 2021): 408. http://dx.doi.org/10.3390/jrfm14090408.

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Food safety is a major risk for agribusiness firms. According to the Centers for Disease Control and Prevention (CDC), approximately 5000 people die annually, and 36,000 people are hospitalized as a result of foodborne outbreaks in the United States. Globally, the death estimate is about 42,000 people per year. A single outbreak could cost a particular segment of the food industry hundreds of millions of dollars due to recalls and liability; these instances might amount to billions of dollars annually. Despite U.S. advancements and regulations, such as pathogen reduction/hazard analysis critical control points (PR/HACCP) in 1996 and the Food Modernization Act in 2010, to reduce food-safety risk, retail meat facilities continue to experience recalls and major outbreaks. We developed a stochastic-optimization framework and used stochastic-dominance methods to evaluate the effectiveness for three strategies that are used by retail meat facilities. Copula value-at-risk (CVaR) was utilized to predict the magnitude of the risk exposure associated with alternative, cost-effective risk-reduction strategies. The results showed that optimal retail-intervention strategies vary by meat and pathogen types, and that having a single Salmonella performance standard for PR/HACCP could be inefficient for reducing other pathogens and food-safety risks.

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13

Hürlimann, Werner. "Analytical Evaluation of Economic Risk Capital for Portfolios of Gamma Risks." ASTIN Bulletin 31, no. 1 (May 2001): 107–22. http://dx.doi.org/10.2143/ast.31.1.996.

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AbstractBased on the notions of value-at-risk and expected shortfall, we consider two functionals, abbreviated VaR and RaC, which represent the economic risk capital of a risky business over some time period required to cover losses with a high probability. These functionals are consistent with the risk preferences of profit-seeking (and risk averse) decision makers and preserve the stochastic dominance order (and the stop-loss order). Quantitatively, RaC is equal to VaR plus an additional stop-loss dependent term, which takes into account the average amount at loss. Furthermore, RaC is additive for comonotonic risks, which is an important extremal situation encountered in the modeling of dependencies in multivariate risk portfolios. Numerical illustrations for portfolios of gamma distributed risks follow. As a result of independent interest, new analytical expressions for the exact probability density of sums of independent gamma random variables are included, which are similar but different to previous expressions by Provost (1989) and Sim (1992).

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14

Han, Chuan-Hsiang, Wei-Han Liu, and Tzu-Ying Chen. "VaR/CVaR Estimation Under Stochastic Volatility Models." SSRN Electronic Journal, 2013. http://dx.doi.org/10.2139/ssrn.2202032.

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15

Bardou, O., N. Frikha, and G. Pagès. "Computing VaR and CVaR using stochastic approximation and adaptive unconstrained importance sampling." Monte Carlo Methods and Applications 15, no. 3 (January 2009). http://dx.doi.org/10.1515/mcma.2009.011.

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16

Wong, Wing-Keung, and Chenghu Ma. "Stochastic Dominance and Risk Measure: A Decision-Theoretic Foundation for VAR and C-Var." SSRN Electronic Journal, 2006. http://dx.doi.org/10.2139/ssrn.907272.

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17

Chang, Chia-Lin, Juan-Angel Jimmnez-Martin, Esfandiar Maasoumi, Michael McAleer, and Teodosio Perez Amaral. "Choosing Expected Shortfall Over VaR in Basel III Using Stochastic Dominance." SSRN Electronic Journal, 2016. http://dx.doi.org/10.2139/ssrn.2746710.

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18

Khor, Cheng Seong, Sara Giarola, Benoit Chachuat, and Nilay Shah. "An Optimization-Based Framework for Process Planning under Uncertainty with Risk Management." Chemical Product and Process Modeling 6, no. 2 (August 2, 2011). http://dx.doi.org/10.2202/1934-2659.1597.

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In the current challenging and volatile political and economic environment, the process industry is exposed to a high degree of uncertainty that renders the production planning task to be a risky and complex optimization problem requiring high computational expense. This work proposes a computationally-tractable optimization-based framework for risk management in midterm process planning under uncertainty. We employ stochastic programming to account for the uncertainty in which a scenario-based approach is used to approximate the underlying probability distribution of the uncertain parameters. The problem is formulated as a recourse-based two-stage stochastic program that incorporates a mean-risk structure in the objective function. Two risk measures are applied, namely Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). However, since a large number of scenarios are often required to capture the stochasticity of the problem, the model suffers from the curse of dimensionality. To circumvent this problem, we propose a computational procedure with a relatively low computational burden that involves the following two major steps. First, a linear programming (LP) approximation of the risk-inclined version of the planning model is solved for a number of randomly generated scenarios. Subsequently, the VaR parameters of the model are simulated and incorporated into a meanCVaR stochastic LP approximation of the risk-averse version of the planning model. The proposed approach is implemented on a petroleum refinery planning case study with satisfactory results that demonstrate how solutions with relatively affordable computational expense can be attained in a risk-averse model in the face of uncertainty. Future work will mainly involve extending the approach to a multiobjective formulation as well as for mixed-integer optimization problems.

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