Skip to main content

On some stochastic optimal impulse control problems

  • Conference paper
  • First Online:
Book cover Recent Mathematical Methods in Dynamic Programming

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1119))

  • 458 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 37.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. BENSOUSSAN, J.L. LIONS: Contrôle impulsionnel et inéquations quasi-variationnelles d’évolution, C.R. Acad. Sc. Paris, 276, série A (1973), 1333–1338.

    MathSciNet  MATH  Google Scholar 

  2. A. BENSOUSSAN, J.L. LIONS: Optimal Impulse and Continuous Control, Method of Nonlinear Quasi Variational Inequalities, Trudy Mat. Inst. Steklov, 134, (1975), 5–22.

    MathSciNet  MATH  Google Scholar 

  3. A. BENSOUSSAN, J.L. LIONS: Contrôle impulsionnel et inéquations quasi-variationnelles, Dunod, Paris (1982).

    MATH  Google Scholar 

  4. A. BENSOUSSAN, J. FREHSE, U. MOSCO: A stochastic impulse control problem with quadratic growth Hamiltonian and corresponding quasi-variational inequality, J. Reine Angew. Math., 331 (1982), 125–145.

    MathSciNet  MATH  Google Scholar 

  5. D.P. BERTSEKAS, S.E. SHREVE: Stochastic optimal control: The discrete time case, Academic Press, New York.

    Google Scholar 

  6. L. CAFFARELLI, A. FRIEDMAN: Regularity of the solution of the Q.V.I. for the impulse control problem, Comm. P.D.E., 3 (1978), 745–753.

    Article  MathSciNet  MATH  Google Scholar 

  7. F. DONATI, M. MATZEU: On the Strong Solutions of some Nonlinear Evolution Problems in Ordered Banach Spaces, Boll. UMI, 5, 16-B (1979), 54–73.

    MathSciNet  MATH  Google Scholar 

  8. W. FLEMING, R. RISHEL: Optimal deterministic and stochastic control, Springer-Verlag, Berlin, 1975.

    Book  MATH  Google Scholar 

  9. J. FREHSE, U. MOSCO: Irregular Obstacle and Quasi-Variational Inequalities of Stochastic Impulse Control, Ann. Sc. Norm. Sup. Pisa, Serive IV, IX, n. 1 (1982), 105–197.

    MathSciNet  MATH  Google Scholar 

  10. A. FRIEDMAN: Stochastic differential equations and applications, Vol. 2, Academic Press, New York, 1976.

    MATH  Google Scholar 

  11. B. HANOUZET, J.L. JOLY: Convergence uniforme des itérés definissant la solution d’une inéquation quasi variationnelle abstraite, C.R. Acad. Sc. Paris, 286, Série A, (1978), 735–738.

    MathSciNet  MATH  Google Scholar 

  12. J.L. JOLY, U. MOSCO, G.M. TROIANIELLO: On the regular solution of a quasi-variational inequality connected to a problem of stochastic impulse control, J. Math. Anal. Appl., 61 (1977), 357–369.

    Article  MathSciNet  MATH  Google Scholar 

  13. N.V. KRYLOV: Controlled diffusion processes, Springer Verlag, Berlin, 1980.

    Book  MATH  Google Scholar 

  14. H. KUSHNER: Probability methods for approximation in stochastic control and elliptic equations, Acad. Press (1977), New York.

    Google Scholar 

  15. O.A. LADYZENSKAJA, V.A. SOLONNIKOV, N.N. URAL’CEVA: Linear and quasilinear Equations of Parabolic Type, Transl. of Math. Monographs, 23 (1968).

    Google Scholar 

  16. M. MATZEU, M.A. VIVALDI: On the regular solution of a nonlinear parabolic quasi-variational inequality related to a stochastic control problem, Comm. P.D.E. (10), 4, (1979), 1123–1147.

    Article  MathSciNet  MATH  Google Scholar 

  17. M. MATZEU, U. MOSCO, M.A. VIVALDI: Sur le problème du contrôle optimal stochastique continu et impulsionnel avec Hamiltonien à croissance quadratique, C.R. Acad. Sc., Paris, t. 296, Séreie I (1983), 817–820.

    Google Scholar 

  18. F. MIGNOT, J.P. PUEL: Inéquations d’évolution paraboliques avec convexes dépendant du temps; applications aux inéquations quasi-variationnelles d’évolution, Arch. Rat. Mech. An. 64 (1977), 59–91.

    Article  MathSciNet  MATH  Google Scholar 

  19. U. MOSCO: Nonlinear quasi-variational inequalities and stochastic impulse control theory, Proc. Conf. Equadiff IV, Praha, 1977, edited by J. Fabéra, Lect. Notes in Math., 703, Springer-Verlag, (1979).

    Google Scholar 

  20. U. MOSCO: On some nonlinear quasi-variational inequalities and implicit complementarity problems in stochastic control theory, in Variational Inequalities, Proc. edited by R.W. Cottle, F. Giannessi and J.L. Lions, J. Wiley.

    Google Scholar 

  21. U. MOSCO: Module de Wiener et estimations du potential pour le problème d’obstacle, C.R. Acad. Sci. Paris, to appear.

    Google Scholar 

  22. U. MOSCO: Obstacle problems: Do continuous solutions exist under wildly irregular constraints? IIASA Publ., to appear.

    Google Scholar 

  23. M.A. VIVALDI: A parabolic quasi-variational inequality related to a stochastic impulse control problem with quadratic growth Hamiltonian, Numer. Funct. Anal. and Optimiz., 4 (3), (1981–82), 241–268.

    Article  MathSciNet  MATH  Google Scholar 

  24. M.A. VIVALDI: Non linear parabolic variational inequalities: existence of weak solutions and regularity properties, to appear.

    Google Scholar 

Download references

Authors

Editor information

Italo Capuzzo Dolcetta Wendell H. Fleming Tullio Zolezzi

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Mosco, U. (1985). On some stochastic optimal impulse control problems. In: Dolcetta, I.C., Fleming, W.H., Zolezzi, T. (eds) Recent Mathematical Methods in Dynamic Programming. Lecture Notes in Mathematics, vol 1119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074784

Download citation

  • DOI: https://doi.org/10.1007/BFb0074784

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15217-0

  • Online ISBN: 978-3-540-39365-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics