# Conditional Value-at-Risk for General Loss Distributions

@article{Rockafellar2001ConditionalVF, title={Conditional Value-at-Risk for General Loss Distributions}, author={R. Tyrrell Rockafellar and Stanislav Uryasev}, journal={Corporate Finance and Organizations eJournal}, year={2001} }

Fundamental properties of conditional value-at-risk, as a measure of risk with significant advantages over value-at-risk, are derived for loss distributions in finance that can involve discreetness. Such distributions are of particular importance in applications because of the prevalence of models based on scenarios and finite sampling. Conditional value-at-risk is able to quantify dangers beyond value-at-risk, and moreover it is coherent. It provides optimization shortcuts which, through…

## 2,574 Citations

Analytical Bounds for two Value-at-Risk Functionals

- EconomicsASTIN Bulletin
- 2002

Abstract Based 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…

Simulating Sensitivities of Conditional Value at Risk

- MathematicsManag. Sci.
- 2009

This paper proves that the CVaR sensitivity can be written as a conditional expectation for general loss distributions, and proposes and demonstrates how to use the estimator to solve optimization problems withCVaR objective and/or constraints, and compares it to a popular linear programming-based algorithm.

Conditional Value-at-Risk Bounds for Compound Poisson Risks and a Normal Approximation

- Computer Science
- 2002

A simple method is presented to bound the conditional value-at-risk of compound Poisson loss distributions under incomplete information about its severity distribution, which is assumed to have a known finite range, mean, and variance.

Conditional Value-at-Risk for Log-Distributions

- Business
- 2018

Conditional Value-at-Risk (CVaR) represents a significant improvement over the Value-at-Risk (VaR) in the area of risk measurement, as it catches the risk beyond the VaR threshold. CVaR is also…

Conditional Value-at-Risk for Elliptical Distributions

- Business
- 2018

Conditional Value-at-Risk (CVaR) represents a significant improvement over the Value-at-Risk (VaR) in the area of risk measurement, as it catches the risk beyond the VaR threshold. CVaR is also…

On closed-form calculation of CVaR

- Engineering
- 2005

Although Conditional Value-at-Risk has significant advantages over traditional risk measures such as Value-at-Risk, it has not been adopted by practitioners as quickly as expected. One of the reasons…

Conditional Value-at-Risk for Uncommon Distributions

- Mathematics
- 2018

Conditional Value-at-Risk (CVaR) represents a significant improvement over the Value-at-Risk (VaR) in the area of risk measurement, as it catches the risk beyond the VaR threshold. CVaR is also…

Value-at-Risk and Conditional Value-at-Risk in Optimization Under Uncertainty

- Computer ScienceUncertainty Management for Robust Industrial Design in Aeronautics
- 2018

The implementation of an efficient risk measure-based optimization algorithm based on the introduction of the weighted empirical cumulative distribution function (WECDF) and on the use of methods for changing the probability measure is discussed.

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

- Economics
- 2008

This tutorial tries to explain strong and weak features of these risk measures and illustrate them with several examples, and demonstrates risk management/optimization case studies conducted with the Portfolio Safeguard package.

## References

SHOWING 1-10 OF 87 REFERENCES

Portfolio optimization with conditional value-at-risk objective and constraints

- Economics
- 2001

Recently, a new approach for optimization of Conditional Value-at-Risk (CVaR) was suggested and tested with several applications. For continuous distributions, CVaR is defined as the expected loss…

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

- Economics
- 2000

The value-at-risk (VaR) and the conditional value-at-risk (CVaR) are two commonly used risk measures. We state some of their properties and make a comparison. Moreover, the structure of the portfolio…

Beyond VaR: from measuring risk to managing risk

- EconomicsProceedings of the IEEE/IAFE 1999 Conference on Computational Intelligence for Financial Engineering (CIFEr) (IEEE Cat. No.99TH8408)
- 1999

This paper examines tools for managing, as opposed to simply monitoring, a portfolio's value-at-risk (VaR), and reviews the parametric, or delta-normal versions of these tools and then extends them to the simulation based, or nonparametric case.

Portfolio Optimization with Drawdown Constraints

- Economics
- 2000

We propose a new one-parameter family of risk measures, which is called Conditional Drawdown-at-Risk (CDaR). These measures of risk are functionals of the portfolio drawdown (underwater) curve…

Risk Management: Correlation and Dependence in Risk Management: Properties and Pitfalls

- Computer Science
- 2002

This article deals with the static (nontime- dependent) case and emphasizes the copula representation of dependence for a random vector and the problem of finding multivariate models which are consistent with prespecified marginal distributions and correlations is addressed.

Optimization of conditional value-at risk

- Economics
- 2000

In an intensifying international competition banks are forced to place increased emphasis on enter-prise wide risk-/return management. Financial risks have to be limited and managed from a bank wide…

Have Your Cake and Eat It, Too: Increasing Returns While Lowering Large Risks!

- Economics
- 1999

In the real world, the variance of portfolio returns provides only a limited quantification of incurred risks, as the distributions of returns have “fat tails” and the dependence between assets are…

Value-at-Risk Based Risk Management: Optimal Policies and Asset Prices

- Economics, Business
- 1999

This paper analyzes optimal, dynamic portfolio and wealth/consumption policies of utility maximizing investors who must also manage market-risk exposure using a given risk-management model. We focus…

Evaluating Value at Risk Methodologies: Accuracy versus Computational Time

- Business
- 1996

Recent research has shown that different methods of computing Value at Risk (VAR) generate widely varying results, suggesting the choice of VAR method is very important. This article examines six VAR…

Risk Management: Value at Risk and Beyond

- Economics
- 2003

Introduction 1. Quantifying the risks of trading: comparing and contrasting the measurement of market risk (VaR) and counterparty exposure Evan Picoult 2. Value at risk analysis of a leveraged swap…