Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk

Pflug, Georg Ch.

doi:10.1007/978-1-4757-3150-7_15

Cited by 521 publications

(310 citation statements)

References 3 publications

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“…Although positive homogeneity is obeyed, the subadditivity is violated. It has been proved, for example, in Acerbi and Tasche [2], Pflug [15], and Rockafellar and Uryasev [20], that for any probability level …”

Section: Risk Measuresmentioning

confidence: 99%

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Value-at-Risk vs. Conditional Value-at-Risk in Risk Management and Optimization

Sarykalin¹

2008

State-of-the-Art Decision-Making Tools in the Information-Intensive Age

256

165

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From the mathematical perspective considered in this tutorial, risk management is a procedure for shaping a risk distribution. Popular functions managing risk are valueat-risk (VaR) and conditional value-at-risk (CVaR). The problem of choice between VaR and CVaR, especially in financial risk management, has been quite popular in academic literature. Reasons affecting the choice between VaR and CVaR are based on the differences in mathematical properties, stability of statistical estimation, simplicity of optimization procedures, acceptance by regulators, etc. This tutorial presents our personal experience working with these key percentile risk measures. We try to explain strong and weak features of these risk measures and illustrate them with several examples. We demonstrate risk management/optimization case studies conducted with the Portfolio Safeguard package.

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Section: Risk Measuresmentioning

confidence: 99%

“…Pflug [15] followed a different approach and suggested to define CVaR via an optimization problem, which he borrowed from Rockafellar and Uryasev [19]:…”

Section: Definition 2 (Conditional Value-at-risk)mentioning

confidence: 99%

Value-at-Risk vs. Conditional Value-at-Risk in Risk Management and Optimization

Sarykalin¹

2008

State-of-the-Art Decision-Making Tools in the Information-Intensive Age

256

165

View full text Add to dashboard Cite

show abstract

“…As established in [17], CVaR has four properties required for a coherent risk measure: subadditivity, positive homogeneity, monotonicity and translation invariance. Moreover, in contrast to VaR, CVaR is convex with respect to portfolio positions, a major practical advantage of CVaR over VaR in applications.…”

Section: B Construction Of Risk Measuresmentioning

confidence: 99%

Financial risk management in restructured wholesale power markets: Concepts and tools

Somani

Tesfatsion

2010

IEEE PES General Meeting

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Abstract-The goal of this tutorial is three-fold: to facilitate cross-disciplinary communication among power engineers and economists by explaining and illustrating basic financial risk management concepts relevant for wholesale power markets (WPMs); to illustrate the complicated and risky strategic decision making required of power traders and risk managers operating in multiple interrelated submarkets comprising modern WPMs; and to briefly discuss the potential of agent-based modeling for the study of this decision making.

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“…It is worth noting that CVaR has various desirable properties as a risk measure in computational and theoretical aspects (see, e.g., Pflug, 2000;Rockafellar and Uryasev, 2002).…”

Section: Conditional Value-at-riskmentioning

confidence: 99%

Constant Rebalanced Portfolio Optimization Under Nonlinear Transaction Costs

Takano

Gotoh

2010

Asia-Pac Financ Markets

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In this paper, we study a multi-period portfolio optimization where conditional value-atrisk (CVaR) is controlled as well as expected return, and the so-called constant rebalancing strategy is employed under nonlinear transaction costs. In general, the optimization of this strategy itself is, however, difficult to attain a globally optimal solution because of the nonconvexity. In addition, nonlinearity of the transaction cost and CVaR functions makes things worse, and even a locally optimal solution may not be reached via a state-of-the-art nonlinear programming solver when the size of the problem is large. In order to provide a practical solution to the highly complex problem, we propose a local search algorithm where linear approximation problems and nonlinear equations are iteratively solved. Computational results are presented, showing that the proposed algorithm attains a good solution in practical time even when a revised version of an existing global optimization approach cannot return any feasible solutions.

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Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk

Cited by 521 publications

References 3 publications

Value-at-Risk vs. Conditional Value-at-Risk in Risk Management and Optimization

Value-at-Risk vs. Conditional Value-at-Risk in Risk Management and Optimization

Financial risk management in restructured wholesale power markets: Concepts and tools

Constant Rebalanced Portfolio Optimization Under Nonlinear Transaction Costs

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