Journal of Optimization Theory and Applications

, Volume 144, Issue 2, pp 335–365 | Cite as

Maximum Principle for Stochastic Control in Continuous Time with Hard End Constraints

  • A. Seierstad


A maximum principle is proved for certain problems of continuous–time stochastic control with hard end constraints (end constraints satisfied a.s.). In the problems, the dynamics (the state differential equation) changes at certain stochastic points in time.


Stochastic maximum principle Hard end constraints 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Arkin, V.I., Evstigneev, L.V.: Stochastic Models of Control and Economic Dynamics. Academic Press, London (1982) Google Scholar
  2. 2.
    Seierstad, A.: Stochastic Control in Discrete and Continuous Time. Springer, New York (2009) MATHCrossRefGoogle Scholar
  3. 3.
    Kushner, H.J.: Necessary conditions for continuous parameter stochastic optimization problem. SIAM J. Control Optim. 10, 550–565 (1972) MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Haussmann, U.G.: A Stochastic Maximum Principle for Optimal Control of Diffusions. Pitman Research Notes in Mathematics Series, vol. 151. Longman, Harlow (1986) MATHGoogle Scholar
  5. 5.
    Peng, S.: A general stochastic maximum principle for optimal control problems. SIAM J. Control Optim. 28, 966–979 (1990) MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Yong, J., Zhou, X.Y.: Stochastic Controls. Hamiltonian Systems and HJB Equations. Springer, New York (1999) MATHGoogle Scholar
  7. 7.
    Dunford, N., Schwartz, J.T.: Linear Operators, Part I. Interscience, New York (1967) Google Scholar
  8. 8.
    Seierstad, A.: Maximum principle for stochastic control in continuous time with hard end constraints. Memorandum from Department of Economics, University of Oslo, No. 24 (2002) Google Scholar
  9. 9.
    Seierstad, A.: A stochastic maximum principle with hard end constraints. Memorandum from Department of Economics, University of Oslo, No. 10 (1991) Google Scholar
  10. 10.
    Seierstad, A.: A local attainability property for control systems defined by nonlinear ordinary differential equations in a Banach space. J. Differ. Equ. 8, 475–487 (1970) MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Seierstad, A.: An extension to Banach space of Pontryagin’s maximum principle. J. Optim. Theory Appl. 17, 293–335 (1975) MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of OsloOsloNorway

Personalised recommendations