PL EN


2013 | 154 | 53-60
Article title

Wielowymiarowa warunkowa wartość zagrożona jako miara ryzyka

Content
Title variants
EN
The Multivariate Conditional Value-At-Risk As a Measure of Risk
Languages of publication
PL
Abstracts
EN
The Multivariate Conditional Value-at-Risk (MCVaR) is a scalar risk measure for multivariate risks modeled by multivariate random variables. It is assumed that the univariate risk components are perfect substitutes, i.e., they are expressed in the same units. MCVaR is a quantile risk measure that allows one to emphasize the consequences of more pessimistic scenarios. By changing the level of the quantile, the measure permits to parameterize prudent attitudes toward risk ranging from extreme risk aversion to risk neutrality. In terms of definition, MCVaR is slightly different from the popular and well-researched Conditional Value-at-Risk (CVaR). Nevertheless, this small difference allows one to efficiently solve MCVaR portfolio optimization problems based on the full information carried by a multivariate random variable using column generation technique, which is not possible in the case of CVaR.
Year
Volume
154
Pages
53-60
Physical description
Contributors
References
  • Andersson F., Mausser H., Rosen D., Uryasev S., Credit risk optimization with Conditional Value-at-Risk criterion. "Mathematical Programming" 2001, No. 89.
  • Artzner P., Delbaen F., Eber J.-M., Heath D., Thinking coherently, "Risk" 1997, No. 10.
  • Artzner P., Delbaen F., Eber J.-M., Heath D., Coherent measures of risk. "Mathematical Finance" 1999, No. 9.
  • Dantzig G.B., Wolfe P., The decomposition algorithm for linear programs, "Econometrica" 1961, No. 29(4).
  • Mansini R., Ogryczak W., Speranza M.G., LP solvable models for portfolio optimization: A classification and computational comparison, "IMA Journal of Management Mathematics" 2003, No. 14.
  • Ogryczak W., Śliwiński T., On solving the dual for portfolio selection by optimizing Conditional Value at Risk, "Computational Optimization and Applications" 2011, No. 50.
  • Pflug G.Ch., Some remarks on the Value-at-Risk and the Conditional Valueat- Risk, in: Probabilistic Constrained Optimization: Methodology and Applications, ed. S. Uryasev, Kluwer A.P., Dordrecht 2000.
  • Rockafellar R.T., Uryasev S., Optimization of Conditional Value-at-Risk. "Journal of Risk" 2000, No. 2.
  • Rockafellar R.T., Uryasev S., Conditional Value-at-Risk for general distributions. "Journal of Banking and Finance" 2002, No. 26.
Document Type
Publication order reference
Identifiers
ISSN
2083-8611
YADDA identifier
bwmeta1.element.desklight-492cf465-ffa1-4084-aa3a-8137634fd447
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.