Risk objectives in two-stage stochastic programming models

Jitka Dupačová

Kybernetika (2008)

  • Volume: 44, Issue: 2, page 227-242
  • ISSN: 0023-5954

Abstract

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In applications of stochastic programming, optimization of the expected outcome need not be an acceptable goal. This has been the reason for recent proposals aiming at construction and optimization of more complicated nonlinear risk objectives. We will survey various approaches to risk quantification and optimization mainly in the framework of static and two-stage stochastic programs and comment on their properties. It turns out that polyhedral risk functionals introduced in Eichorn and Römisch [Eich-Ro] have many convenient features. We shall complement the existing results by an application of contamination technique to stress testing or robustness analysis of stochastic programs with polyhedral risk objectives with respect to the underlying probability distribution. The ideas will be illuminated by numerical results for a bond portfolio management problem.

How to cite

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Dupačová, Jitka. "Risk objectives in two-stage stochastic programming models." Kybernetika 44.2 (2008): 227-242. <http://eudml.org/doc/33923>.

@article{Dupačová2008,
abstract = {In applications of stochastic programming, optimization of the expected outcome need not be an acceptable goal. This has been the reason for recent proposals aiming at construction and optimization of more complicated nonlinear risk objectives. We will survey various approaches to risk quantification and optimization mainly in the framework of static and two-stage stochastic programs and comment on their properties. It turns out that polyhedral risk functionals introduced in Eichorn and Römisch [Eich-Ro] have many convenient features. We shall complement the existing results by an application of contamination technique to stress testing or robustness analysis of stochastic programs with polyhedral risk objectives with respect to the underlying probability distribution. The ideas will be illuminated by numerical results for a bond portfolio management problem.},
author = {Dupačová, Jitka},
journal = {Kybernetika},
keywords = {two-stage stochastic programs; polyhedral risk objectives; robustness; contamination; bond portfolio management problem; two-stage stochastic programs; polyhedral risk objectives; robustness; contamination; bond portfolio management problem},
language = {eng},
number = {2},
pages = {227-242},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Risk objectives in two-stage stochastic programming models},
url = {http://eudml.org/doc/33923},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Dupačová, Jitka
TI - Risk objectives in two-stage stochastic programming models
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 2
SP - 227
EP - 242
AB - In applications of stochastic programming, optimization of the expected outcome need not be an acceptable goal. This has been the reason for recent proposals aiming at construction and optimization of more complicated nonlinear risk objectives. We will survey various approaches to risk quantification and optimization mainly in the framework of static and two-stage stochastic programs and comment on their properties. It turns out that polyhedral risk functionals introduced in Eichorn and Römisch [Eich-Ro] have many convenient features. We shall complement the existing results by an application of contamination technique to stress testing or robustness analysis of stochastic programs with polyhedral risk objectives with respect to the underlying probability distribution. The ideas will be illuminated by numerical results for a bond portfolio management problem.
LA - eng
KW - two-stage stochastic programs; polyhedral risk objectives; robustness; contamination; bond portfolio management problem; two-stage stochastic programs; polyhedral risk objectives; robustness; contamination; bond portfolio management problem
UR - http://eudml.org/doc/33923
ER -

References

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  1. Acerbi C., Spectral measures of risk: A coherent representation of subjective risk aversion, J. Bank. Finance 26 (2002), 1505–1518 
  2. Ahmed S., Convexity and decomposition of mean-risk stochastic programs, Math. Programming A 106 (2006), 447–452 Zbl1134.90025MR2216788
  3. Artzner P., Delbaen F., Eber, J., Heath D., Coherent measures of risk, Math. Finance 9 (1999), 203–228. See also , pp. 145–175 (1999) Zbl0980.91042MR1850791
  4. Bertocchi M., Dupačová, J., Moriggia V., Sensitivity analysis of a bond portfolio model for the Italian market, Control Cybernet. 29 (2000), 595–615 Zbl1017.91036
  5. Bertocchi M., Moriggia, V., Dupačová J., Horizon and stages in applications of stochastic programming in finance, Ann. Oper. Res. 142 (2006), 63–78 Zbl1101.90043MR2222910
  6. Dempster M. A. H., ed., Risk Management: Value at Risk and Beyond, Cambridge Univ. Press, Cambridge 2002 Zbl1213.91087MR1892188
  7. Dupačová J., Stability in stochastic programming with recourse – contaminated distributions, Math. Programing Stud. 27 (1986), 133–144 (1986) Zbl0594.90068MR0836754
  8. Dupačová J., Stability and sensitivity analysis in stochastic programming, Ann. Oper. Res. 27 (1990), 115–142 (1990) MR1088990
  9. Dupačová J., Postoptimality for multistage stochastic linear programs, Ann. Oper. Res. 56 (1995), 65–78 (1995) Zbl0838.90089MR1339785
  10. Dupačová J., Scenario based stochastic programs: Resistance with respect to sample, Ann. Oper. Res. 64 (1996), 21–38 (1996) Zbl0854.90107MR1405628
  11. Dupačová J., Reflections on robust optimization, In: Stochastic Programming Methods and Technical Applications (K. Marti and P. Kall, eds.), LNEMS 437, Springer, Berlin 1998, pp. 111–127 (1998) Zbl0909.90218MR1650772
  12. Dupačová J., Stress testing via contamination, In: Coping with Uncertainty. Modeling and Policy Issues (K. Marti et al., eds.), LNEMS 581, Springer, Berlin 2006, pp. 29–46 Zbl1151.90504MR2278935
  13. Dupačová J., Contamination for multistage stochastic programs, In: Prague Stochastics 2006 (M. Hušková and M. Janžura, eds.), Matfyzpress, Praha 2006, pp. 91–101. See also SPEPS 2006-06 
  14. Dupačová J., Bertocchi, M., Moriggia V., Testing the structure of multistage stochastic programs, Submitted to Optimization Zbl1168.90567
  15. Dupačová J., Hurt, J., Štěpán J., Stochastic Modeling in Economics and Finance, Part II, Kluwer Academic Publishers, Dordrecht 2002 MR2008457
  16. Dupačová J., Polívka J., Stress testing for VaR and CVaR, Quantitative Finance 7 (2007), 411–421 Zbl1180.91163MR2354778
  17. Eichhorn A., Römisch W., Polyhedral risk measures in stochastic programming, SIAM J. Optim. 16 (2005), 69–95 Zbl1114.90077MR2177770
  18. Eichhorn A., Römisch W., Mean-risk optimization models for electricity portfolio management, In: Proc. 9th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS 2006), Stockholm 2006 
  19. Eichhorn A., Römisch W., Stability of multistage stochastic programs incorporating polyhedral risk measures, To appear in Optimization 2008 Zbl1192.90131MR2400373
  20. Föllmer H., Schied A., Stochastic Finance, An Introduction in Discrete Time. (De Gruyter Studies in Mathematics 27). Walter de Gruyter, Berlin 2002 Zbl1126.91028MR1925197
  21. Kall P., Mayer J., Stochastic Linear Programming, Models, Theory and Computation. Springer-Verlag, Berlin 2005 Zbl1211.90003MR2118904
  22. Mulvey J. M., Vanderbei R. J., Zenios S. A., Robust optimization of large scale systems, Oper. Res. 43 (1995), 264–281 (1995) Zbl0832.90084MR1327415
  23. Ogryczak W., Ruszczyński A., Dual stochastic dominance and related mean-risk models, SIAM J. Optim. 13 (2002), 60–78 Zbl1022.91017MR1922754
  24. Pflug G. Ch., Some remarks on the Value-at-Risk and the Conditional Value-at-Risk, In: Probabilistic Constrained Optimization, Methodology and Applications (S. Uryasev, ed.), Kluwer Academic Publishers, Dordrecht 2001, pp. 272–281 Zbl0994.91031MR1819417
  25. Pflug G. Ch., Römisch W., Modeling, Measuring and Managing Risk, World Scientific, Singapur 2007 Zbl1153.91023MR2424523
  26. Rockafellar R. T., Uryasev S., Conditional value-at-risk for general loss distributions, J. Bank. Finance 26 (2001), 1443–1471 
  27. Rockafellar R. T., Uryasev, S., Zabarankin M., Generalized deviations in risk analysis, Finance Stochast. 10 (2006), 51–74 Zbl1150.90006MR2212567
  28. Römisch W., Stability of stochastic programming problems, Chapter 8 in , pp. 483–554 MR2052760
  29. Römisch W., Wets R. J-B., Stability of ε -approximate solutions to convex stochastic programs, SIAM J. Optim. 18 (2007), 961–979 Zbl1211.90151MR2345979
  30. Ruszczyński A., Shapiro A., eds., Handbook on Stochastic Programming, Handbooks in Operations Research & Management Science 10, Elsevier, Amsterdam 2002 
  31. Ruszczyński A., Shapiro A., Optimization of risk measures, Chapter 4 in: Probabilistic and Randomized Methods for Design under Uncertainty (G. Calafiore and F. Dabbene, eds.), Springer, London 2006, pp. 121–157 Zbl1181.90281

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