Central European Journal of Operations Research

, Volume 20, Issue 4, pp 623–632 | Cite as

CVaR minimization by the SRA algorithm

  • Kolos Cs. ÁgostonEmail author
Original Paper


Using the risk measure CVaR in financial analysis has become more and more popular recently. In this paper we apply CVaR for portfolio optimization. The problem is formulated as a two-stage stochastic programming model, and the SRA algorithm, a recently developed heuristic algorithm, is applied for minimizing CVaR.


Risk measure CVaR Stochastic programming Numerical optimization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andersson F, Mausser H, Rosen D, Uryasev S (2001) Credit risk optimization with conditional value-at-risk criterion. Math Program Ser B 89: 273–291CrossRefGoogle Scholar
  2. Artzner P, Delbaen F, Eber J-M, Heath D (1999) Coherent measures of risk. Math Finance 9(3): 203–228CrossRefGoogle Scholar
  3. Deák I (2001) Successive regression approximations for solving equations. Pure Math Appl 12: 25–50Google Scholar
  4. Deák I (2002) Computing two-stage stochastic programming problems by successive regression approximations. In: Mart K (eds) Stochastic optimization techniques: numerical methods and technical applications, vol 513. Springer, LNEMS, pp 91–102Google Scholar
  5. Deák I (2003) Solving stochastic programming problems by successive regression approximations-numerical results. In: Marti K, Ermoliev Y, Pflug G (eds) Dynamic stochastic optimization, vol 532. Springer, LNEMS, pp 209–224Google Scholar
  6. Deák I (2006) Two-stage stochastic problems with correlated normal variables: computational experiences. Ann Oper Res 142: 79–97CrossRefGoogle Scholar
  7. Deák I (2010) Convergence of succesive regression approximations for solving noisy equations. In: Topping BHV, Adam JM , Pallarés FJ, Bru R, Romero ML (eds) Proceedings of the tenth international conference on computational structures technology, Civil-Comp Press, Stirlingshire, UK, Paper 209Google Scholar
  8. Fábián Cs, Veszprémi A (2006) Algorithms for handling CVaR-constraints in dynamic stochastic programming models with applications to finance. J Risk 10: 111–131Google Scholar
  9. Künzi-Bay A, Mayer J (2006) Computational aspect of minimizing conditional value-at-risk. Comput Manag Sci 3: 3–27CrossRefGoogle Scholar
  10. Mak W-K, Morton D, Wood R (1999) Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper Res Lett 24(1): 47–56CrossRefGoogle Scholar
  11. Pflug G (2000) Some remarks on the value-at-risk and the conditional value-at-risk. In: Uryasev S (eds) Probabilistic constrained optimization. Kluwer, Dordrecht, pp 272–281Google Scholar
  12. Prékopa A (1995) Stochastic programming. Kluwer, Akademiai KiadoGoogle Scholar
  13. Rockafellar T, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2(3): 21–41Google Scholar
  14. Rockafellar T, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J Bank Finance 26: 1443–1471CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Corvinus University of BudapestBudapestHungary

Personalised recommendations