Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition

References

• Ahmed S. Convexity and decomposition of mean-risk stochastic programs. Math. Programming (2006) 106(3):433–446Crossref, Google Scholar
• Artzner P., Delbaen F., Eber J.-M., Heath D. Coherent measures of risk. Math. Finance (1999) 9(3):203–228Crossref, Google Scholar
• Artzner P., Delbaen F., Eber J.-M., Heath D., Ku H. Coherent multiperiod risk adjusted values and Bellman's principle. Ann. Oper. Res. (2007) 152(1):5–22Crossref, Google Scholar
• Birge J. R., Louveaux F. V. A multicut algorithm for two-stage stochastic linear programs. Eur. J. Oper. Res. (1988) 34(3):384–392Crossref, Google Scholar
• Birge J. R., Louveaux F. V.Introduction to Stochastic Programming (1997) (Springer, New York) Google Scholar
• Cheridito P., Delbaen F., Kupper M. Dynamic monetary risk measures for bounded discrete-time processes. Electronic J. Probab. (2006) 11:57–106Crossref, Google Scholar
• Föllmer H., Schied A.Stochastic Finance. An Introduction in Discrete Time (2004) (Walter de Gruyter, Berlin) Crossref, Google Scholar
• Fritelli M., Rosazza Gianin E. Putting order in risk measures. J. Banking Finance (2002) 26(7):1473–1486Crossref, Google Scholar
• Fritelli M., Scandolo G. Risk measures and capital requirements for processes. Math. Finance (2006) 16(4):589–612Crossref, Google Scholar
• Hiriart-Urruty J.-B., Lemaréchal C.Convex Analysis and Minimization Algorithms (1993) (Springer, Berlin) Crossref, Google Scholar
• Kall P., Mayer J.Stochastic Linear Programming (2005) (Springer, New York) Google Scholar
• Ogryczak W., Ruszczyński A. From stochastic dominance to mean-risk models: Semideviations as risk measures. Eur. J. Oper. Res. (1999) 116(1):33–50Crossref, Google Scholar
• Ogryczak W., Ruszczyński A. On consistency of stochastic dominance and mean-semideviation models. Math. Programming (2001) 89(2):217–232Crossref, Google Scholar
• Ogryczak W., Ruszczyński A. Dual stochastic dominance and related mean-risk models. SIAM J. Optim. (2002) 13(1):60–78Crossref, Google Scholar
• Pflug G. Ch., Römisch W.Modeling, Measuring and Managing Risk (2007) (World Scientific, Singapore) Crossref, Google Scholar
• Riedel F. Dynamic coherent risk measures. Stochastic Processes Appl. (2004) 112(2):185–200Crossref, Google Scholar
• Rockafellar R. T., Wets R. J.-B.Variational Analysis (1998) (Springer, Berlin) Crossref, Google Scholar
• Rockafellar R. T., Uryasev S., Zabarankin M. Deviation measures in risk analysis and optimization. Finance Stochastics (2006) 10:51–74Crossref, Google Scholar
• Ruszczyński A. A regularized decomposition method for minimizing a sum of polyhedral functions. Math. Programming (1986) 35(3):309–333Crossref, Google Scholar
• Ruszczyński A., Ruszczyński A., Shapiro A. Decomposition methods. Stochastic Programming (2003) (Elsevier, Amsterdam) Crossref, Google Scholar
• Ruszczyński A.Nonlinear Optimization (2006) (Princeton University Press, Princeton, NJ) Crossref, Google Scholar
• Ruszczyński A. Risk-averse dynamic programming for Markov decision processes. Math. Programming, Ser. B (2010) 125(2):235–261Crossref, Google Scholar
• Ruszczyński A., Shapiro A., Calafiore G., Dabbene F. Optimization of risk measures. Probabilistic and Randomized Methods for Design Under Uncertainty (2005) (Springer, London) Google Scholar
• Ruszczyński A., Shapiro A. Optimization of convex risk functions. Math. Oper. Res. (2006a) 31(3):433–452Link, Google Scholar
• Ruszczyński A., Shapiro A. Conditional risk mappings. Math. Oper. Res. (2006b) 31:544–561Link, Google Scholar
• Scandolo G. Risk measures in a dynamic setting. (2003) . Ph.D. thesis, Università degli Studi di Milano, MilanGoogle Scholar
• Schultz R., Tiedemann S. Risk aversion via excess probabilities in stochastic programs with mixed-integer recourse. SIAM J. Optim. (2003) 14(1):115–138Crossref, Google Scholar
• Schultz R., Tiedemann S. Conditional value-at-risk in stochastic programs with mixed-integer recourse. Math. Programming (2006) 105(2-3):365–386Crossref, Google Scholar
• Shapiro A., Dentcheva D., Ruszczyński A.Lectures on Stochastic Programming: Modeling and Theory (2009) (SIAM, Philadelphia) Crossref, Google Scholar
• Van Slyke R., Wets R. J.-B. L-shaped linear programs with applications to optimal control and stochastic programming. SIAM J. Appl. Math. (1969) 17(4):638–663Crossref, Google Scholar