67
Views
44
CrossRef citations to date
0
Altmetric
Original Articles

On stochastic programming ii: dynamic problems under riskFootnote

Pages 15-42 | Received 23 Dec 1986, Published online: 04 Apr 2007

References

  • Arkin , V.I. 1984 . “ The stochastic maximum principle ” . In Soviet Abstracts of the International Conference on Stochastic Optimization, Kiev, 1984 21 – 23 . V. I. Glushkov Institute, Ukranian Academy of Sciences, Kiev, USSR
  • Arkin , V.I. and Evstigneev , I.V. 1987 . Stochastic Models of Control and Economic Dynamics Nauka, , Moscow (in Russian). English translation by E. A. Medova-Dempster and M. A. H. Dempster. Academic, London and New York, 1987
  • Back , K. and Pliska , S.R. 1987 . The shadow price of information in continuous time decision problems . Stochastics , 22 : 151 – 186 .
  • Bertsekas , D.P. and Shreve , S.E. 1978 . Stochastic Optimal Control: The Discrete Time Case , New York : Academic .
  • Birge , J.R. 1985 . Decomposition and partitioning methods for multi-stage stochastic linear programs . Operations Research , 33 : 989 – 1007 .
  • Birge , J.R. and Wets , R.J.B. 1986 . Designing approximation schemes for stochastic optimization problems, in particular stochastic programs with recourse . Mathematical Programming Studies , 27 : 54 – 102 .
  • Bordunov , N.N. , ed. 1983 . “ On a general stochastic economic dynamics model. In ” . In Models and Methods of Stochastic Optimization 27 – 60 . Moscow (In Russian) Central Economic Mathematics Institute
  • Clarke , F.H. , ed. 1983 . Optimization and Nonsmooth Analysis , New York : Wiley .
  • Dellacherie , C. and Meyer , P.A. 1982 . Probabilities and Potential B: Theory of Martingales North Holland, Amsterdam
  • Dempster , M.A.H. 1968 . On stochastic programming: I. Static linear programming under risk . J. Math. Anal. Applns , 21 : 304 – 343 .
  • Dempster , M.A.H. 1980 . “ Introduction to stochastic programming. In ” . In Stochastic Programming Edited by: Dempster , M.A.H. 3 – 59 . London Academic
  • Dempster , M.A.H. 1981 . “ The expected value of perfect information in the optimal evolution of stochastic problems. In ” . In Stochastic Differential Systems , Edited by: Arato , M. , Vermes , D. and Balakrishnan , A.V. 25 – 40 . Berlin : Springer .
  • Dynkin , E.B. and Yushkevitch , A.A. 1977 . Controlled Markov Processes and Their Applications , Berlin : Springer .
  • Eisner , M.J. and Olsen , P.L. 1975 . Duality for stochastic programming interpreted as L.P. in L-space . SIAM J. Appl. Math , 28 : 779 – 792 .
  • Eisner , M.J. and Olsen , P.L. 1980 . “ Duality in probabilistic programming. In ” . In Stochastic Programming, op. cit 147 – 158 .
  • Evstigneev , I.V. 1976 . “ Lagrange multipliers for the problem of stochastic programming. In ” . In Warsaw Fall Seminars in Mathematical Economics , Edited by: Los , M.W. , Los , J. and Wieczorck , A. 34 – 48 . Berlin : Springer . Lecture Notes in Economics and Mathematical Systems 144
  • Flam , S.D. 1986 . “ Asymptotically stable solutions to stochastic optimization problems. In ” . In Stochastic Programming , Edited by: Archetti , F. , Di Pillo , G. and Lucertini , M. 184 – 193 . Berlin : Springer . Lecture Notes in Information and Control 76
  • Gihman , I.I. and Skorohod , A.V. 1979 . Controlled Stochastic Processes , Berlin : Springer . Naukova Dumka, Kiev, 1977. (In Russian.) English translation
  • Hiriart-Urruty , J.-B. 1982 . Extension of Lipschitz integrands and minimization of nonconvex integral functionals: Applications to the optimal recourse problem in discrete time . Probability and Math Stats , 3 : 19 – 36 .
  • Klein Haneveld , W.K. , ed. 1986 . Duality in Stochastic Linear and Dynamic Programming , Berlin : Springer . Lecture Notes in Economics and Mathematical Systems 274
  • Komlos , J. 1967 . A generalization of a problem of Steinhaus . Acta Math. Acad. Sci. Hungar , 18 : 217 – 229 .
  • Kushner , H.J. 1972 . “ Necessary conditions for discrete parameter stochastic optimization problems. In ” . In Proc. Sixth Berkeley Symp. Math. Stats, and Prob Edited by: Neyman , J. 667 – 685 . Berkeley University of California
  • Kushner , H.J. 1984 . Approximation and Weak Convergence Methods for Random Processes: With Applications to Stochastic Systems Theory , Cambridge, MA : M.I.T. Press .
  • Pliska , S.R. 1982 . “ Duality theory for some stochastic control problems. In ” . In Proceedings of the Second Bad Honef Conference on Stochastic Differential Systems , Edited by: Vogel , W. and Kohlmann , M. 229 – 337 . Berlin : Springer . Lecture Notes in Information and Control 41
  • Rockafellar , R.T. 1976 . Integral Functionals, Normal Integrands and Measurable Selections , Berlin : Springer . Lecture Notes in Mathematics 543
  • Rockafellar , R.T. and Wets , J.-B. 1975 . Stochastic convex programming: Kuhn-Tucker conditions . J. Math. Econ , 2 : 349 – 370 .
  • Rockafellar , R.T. and Wets , J.-B. 1976 . Stochastic convex programming: Basic duality . Pacific J. Math , 62 : 173 – 195 .
  • Rockafellar , R.T. and Wets , J.-B. 1976 . Stochastic convex programming: Relatively complete recourse and induced feasibility . SIAM J. Opt , 14 : 574 – 589 .
  • Rockafellar , R.T. and Wets , J.-B. 1976 . Nonanticipativity and L1-martingales in stochastic optimization problems . Math. Prog. Study , 6 : 170 – 186 .
  • Rockafellar , R.T. and Wets , J.-B. 1978 . The optimal recourse problem in discrete time: L1-multipliers for inequality constraints . SIAM J. Control Opt , 16 : 16 – 36 .
  • Rockafellar , R.T. and Wets , J.-B. 1982 . On the interchange of subdifferentiation and conditional expectation for convex functionals . Stochastics , 7 : 173 – 182 .
  • Rockafellar , R.T. and Wets , J.-B. 1983 . Deterministic and stochastic optimization problems of Bolza type in discrete time . Stochastics , 10 : 273 – 312 .
  • Rota , G.-C . 1960 . On the representation of averaging operators . Rendiconti del Sem. Mat. della U. di Padova , 30 : 52 – 64 .
  • Wets , R.J.-B. 1983 . “ Stochastic programming: Solution techniques and approximation schemes. In ” . In Mathematical Programming: The State of the Art , Edited by: Bachem , A. , Grotschel , M. and Korte , B. 566 – 603 . Berlin : Springer .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.