Optimization with multivariate stochastic dominance constraints

Mathematical Programming

Volumn 117, Issue 1-2, 2009, Pages 111-127

  Dentcheva, Darinka ^a   Ruszczyński, Andrzej ^b  

^a Stevens Institute of Technology   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

Duality; Optimality; Risk; Stochastic order; Utility

Indexed keywords

CONSTRAINED OPTIMIZATION; DESCRIBING FUNCTIONS; LAGRANGE MULTIPLIERS; RISK PERCEPTION; STOCHASTIC PROGRAMMING; TRAJECTORIES; VECTORS;

DUALITY RELATIONS; LAG RANGE; NECESSARY AND SUFFICIENT CONDITIONS; NECESSARY CONDITIONS OF OPTIMALITY; NEUMANN-MORGENSTERN; NON-CONVEX PROBLEMS; OPTIMALITY; OPTIMIZ ATION PROBLEMS; RANDOM VECTORS; SPRINGER (CO); STOCHASTIC DOMINANCE (SD); STOCHASTIC OPTIMIZATION PROBLEMS; STOCHASTIC ORDER; STOCHASTIC ORDERINGS; UNIVARIATE; UTILITY FUNCTIONS (UFS);

OPTIMIZATION;

EID: 46749102111     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-007-0165-x     Document Type: Article

References (26)

1. Berleant, D., Dancre, M., Argaud, J.-P., Sheble, G.: Electric company portfolio optimization under interval stochastic dominance constraints. Proceedings of the fourth international symposium on imprecise probabilities and their applications, Pittsburgh (2005)
2. Billingsley P. (1995). Probability and Measure. Wiley, New York
3. Bonnans J.F. and Shapiro A. (2000). Perturbation Analysis of Optimization Problems. Springer, New York
4. Castaing C. and Valadier M. (1977). Convex Analysis and Measurable Multifunctions. Springer, Berlin
5. Dentcheva D. and Ruszczyński A. (2003). Optimization with stochastic dominance constraints. SIAM J. Optim. 14: 548-566
6. Dentcheva D. and Ruszczyński A. (2004). Optimality and duality theory for stochastic optimization problems with nonlinear dominance constraints. Math. Program. 99: 329-350
7. Dentcheva D. and Ruszczyński A. (2006). Portfolio optimization with stochastic dominance constraints. J. Banking Finance 30(2): 433-451
8. Dudley R.M. (2002). Real Analysis and Probability. Cambridge University Press, Cambridge
9. El Karoui N. and Meziou A. (2006). Constrained optimization with respect to stochastic dominance: applications to portfolio insurance. Math. Finance 16: 103-117
10. Fishburn P.C. (1970). Utility Theory for Decision Making. Wiley, New York
11. Hadar J. and Russell W. (1969). Rules for ordering uncertain prospects. Am. Econ. Rev. 59: 25-34
12. Klatte D. and Henrion R. (1998). Regularity and stability in nonlinear semi-infinite optimization. Nonconvex Optim. Appl. 25: 69-102
13. Lehmann E. (1955). Ordered families of distributions. Ann. Math. Stat. 26: 399-419
14. Levin, V.L.: Convex Analysis in Spaces of Measurable Functions and Its Applications in Economics (in Russian). Nauka, Moscow (1985)
15. Luc D.T. (1989). Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems. Springer, Berlin
16. Mann H.B. and Whitney D.R. (1947). On a test of whether one of two random variables is stochastically larger than the other. Ann. Math. Stat. 18: 50-60
17. Marshall A.W. and Olkin I. (1979). Inequalities: Theory of Majorization and Its Applications. Academic, San Diego
18. Mosler, K., Scarsini,M. (eds.): (1991). Stochastic Orders and Decision Under Risk. Institute of Mathematical Statistics, Hayward, California
19. Müller A. and Stoyan D. (2002). Comparison Methods for Stochastic Models and Risks. Wiley, Chichester
20. Ogryczak W. and Ruszczyński A. (1999). From stochastic dominance to mean-risk models: semideviations as risk measures. Eur. J. Oper. Res. 116: 33-50
21. Quirk J.P. and Saposnik R. (1962). Admissibility and measurable utility functions. Rev. Econ. Stud. 29: 140-146
22. Robinson S.M. (1976). Stability theory for systems of inequalities. II: Differentiable nonlinear systems. SIAM J. Numer. Anal. 13: 497-513
23. Rockafellar R.T. and Wets R.J.-B. (1998). Variational Analysis. Springer, Berlin
24. Ruszczyński, A., Shapiro, A. (eds.): Stochastic Programming. Elsevier, Amsterdam (2003)
25. Shaked M. and Shanthikumar J.G. (1994). Stochastic Orders and Their Applications. Academic, Boston
26. Szekli R. (1995). Stochastic Ordering and Dependence in Applied Probability. Springer, New York