Optimization of Risk Measures
We consider optimization problems involving coherent risk measures. We derive necessary and sufficient conditions of optimality for these problems, and we discuss the nature of the nonanticipativity constraints. Next, we introdice dynamic risk measures, and we formulate multistage optimization problems involving these measures. Conditions similar to dynamic programming equations are developed. The theoretical considerations are illustrated with many examples of mean-risk models applied in practice.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Acerbi, Carlo & Tasche, Dirk, 2002.
"On the coherence of expected shortfall,"
Journal of Banking & Finance,
Elsevier, vol. 26(7), pages 1487-1503, July.
- Riedel, Frank, 2004.
"Dynamic coherent risk measures,"
Stochastic Processes and their Applications,
Elsevier, vol. 112(2), pages 185-200, August.
- W. Ogryczak & A. Ruszczynski, 1997.
"From Stochastic Dominance to Mean-Risk Models: Semideviations as Risk Measures,"
ir97027, International Institute for Applied Systems Analysis.
- Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July.
- Andrzej Ruszczynski & Alexander Shapiro, 2004. "Conditional Risk Mappings," Risk and Insurance 0404002, EconWPA, revised 08 Oct 2005.
- Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
- Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, EconWPA, revised 08 Oct 2005.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpri:0407002. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.