Optimization problems with second order stochastic dominance constraints: Duality, compact formulations, and cut generation methods

SIAM Journal on Optimization

Volumn 19, Issue 3, 2008, Pages 1326-1343

  Rudolf, Gábor ^a   Ruszczyński, Andrzej ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Cutting plane methods; Duality; Stochastic dominance; Stochastic programming

Indexed keywords

COMPACT FORMULATIONS; CUT GENERATION METHOD; CUTTING PLANE METHODS; DUALITY; DUALITY THEORY; FINITE CONVERGENCE; GENERALIZED TRANSPORTATION PROBLEMS; MARGINALS; NEW FORMS; NUMERICAL RESULTS; OPTIMIZATION PROBLEMS; PROBABILITY SPACES; REAL LINE; SECOND ORDERS; STOCHASTIC DOMINANCE; STOCHASTIC OPTIMIZATION PROBLEMS;

STOCHASTIC PROGRAMMING;

EID: 69649091580     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/070702473     Document Type: Article

References (34)

1. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows. Theory, Algorithms, and Applications, Prentice-Hall, Bnglewood Cliffs, NJ, 1993.
2. P. Artzner, F. Delbaen, J.-M. Eber, and D. Heath, Coherent measures of risk, Math. Finance, 9 (1999), pp. 203-228.
3. J. F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems, Springer-Verlag, New York, 2000.
4. D. Dentcheva and A. Ruszczyński, Optimization with stochastic dominance constraints, SIAM J. Optim., 14 (2003), pp. 548-566.
5. D. Dentcheva and A. Ruszczyński, Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints, Math. Program., 99 (2004), pp. 329-350.
6. D. Dentcheva and A. Ruszczyński, Semi-infinite probabilistic optimization: First order stochastic dominance constraints, Optim., 53 (2004), pp. 583-601. (Pubitemid 40190089)
7. D. Dentcheva and A. Ruszczyński, Inverse stochastic dominance constraints and rank dependent expected utility theory, Math. Program., 108 (2006), pp. 297-311.
8. D. Dentcheva and A. Ruszczyński, Portfolio optimization with stochastic dominance constraints, J. Banking Finance, 30 (2006), pp. 433-451.
9. H. Föllmer and A. Schied, Convex measures of risk and trading constraints, Finance Stoch., 6 (2002), pp. 429-447.
10. H. Föllmer and A. Schied, Stochastic Finance. An Introduction in Discrete Time, Walter de Gruyter, Berlin, 2004.
11. L. R. Ford and D. R. Fulkerson, Maximal flow through a network, Canad. J. Math., 8 (1956), pp. 399-404.
12. R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, Duxbury Press, Belmont, CA, 2002.
13. D. Gale, A theorem on flows in networks, Pacific J. Math., 7 (1957), pp. 1073-1082.
14. J. Hadar and W. Russell, Rules for ordering uncertain prospects, Amer. Econ. Rev., 59 (1969), pp. 25-34.
15. ILOG CPLEX 9.0 Users Manual, ILOG, Incline Village, NV, 2005.
16. W. K. Klein Haneveld, Duality in Stochastic Linear and Dynamic Programming, Lecture Notes in Econom. Math. Systems 274, Springer-Verlag, New York, 1986.
17. W. K. Klein Haneveld and M. H. Van Der Vlerk, Integrated chance constraints: Reduced forms and an algorithm, Comput. Manag. Sci., 3 (2006), pp. 245-269.
18. E. Lehmann, Ordered families of distributions, Ann. Math. Statist., 26 (1955), pp. 399-419.
19. H. B. Mann and D. R. Whitney, On a test of whether one of two random variables is stochastically larger than the other, Ann. Math. Statist., 18 (1947), pp. 50-60.
20. N. Miller and A. Ruszczyński, Risk-adjusted probability measures in portfolio optimization with coherent measures of risk, Eur. J. Oper. Res., 191 (2008), pp. 193-206.
21. A. Müller and D. Stoyan, Comparison Methods for Stochastic Models and Risks, John Wiley & Sons, Chichester, 2002.
22. N. Noyan, G. Rudolf, and A. Ruszczyński, Relaxations of linear programming problems with first order stochastic dominance constraints, Oper. Res. Lett., 34 (2006), pp. 653-659.
23. N. Noyan and A. Ruszczyński, Valid inequalities and restrictions for stochastic programming problems with first order stochastic dominance constraints, Math. Program., 114 (2008), pp. 249-275.
24. W. Ogryczak and A. Ruszczyński, From stochastic dominance to mean-risk models: Semideviations as risk measures, Eur. J. Oper. Res., 116 (1999), pp. 33-50.
25. W. Ogryczak and A. Ruszczyński, On consistency of stochastic dominance and meansemideviation models, Math. Program., 89 (2001), pp. 217-232.
26. W. Ogryczak and A. Ruszczyński, Dual stochastic dominance and related mean-risk models, SIAM J. Optim., 13 (2002), pp. 60-78.
27. J. P. Quirk and R. Saposnik, Admissibility and measurable utility functions, Rev. Econ. Stud., 29 (1962), pp. 140-146.
28. R. T. Rockafellar, Conjugate Duality and Optimization, SIAM, Philadelphia, 1974.
29. R. T. Rockafellar and S. Uryasev, Conditional value-at-risk for general loss distributions, J. Banking Finance, 26 (2002), pp. 1443-1471.
30. A. Ruszczynski and A. Shapiro, EDS., Stochastic Programming, Handbooks Oper. Res. Management Sci. 10, Elsevier, Amsterdam, 2003, North Holland.
31. A. Ruszczyński and A. Shapiro, Optimization of convex risk functions, Math. Oper. Res., 31 (2006), pp. 433-452.
32. M. Shared and J. G. Shanthikumar, Stochastic Orders and Their Applications, Academic Press, Boston, 1994.
33. V. Strassen, The existence of probability measures with given marginals, Ann. Math. Statist., 38 (1965), pp. 423-439.
34. M. E. Yaari, The dual theory of choice under risk, Econometrica, 55 (1987), pp. 95-115.