Related Topics

  • Joël Blot
  • Naïla Hayek
Chapter
Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Abstract

Stochastic setting. For the Pontryagin principles of the discrete-time infinite-horizon stochastic optimal control, the pioneering work is that of G. Chow [see the reference in Blot (Nonlinear Anal.: Theor. Meth. Appl. 71(12), e999–e1004 (2009))]. For the scalar case there exists such a principle in Blot (Nonlinear Anal.: Theor. Meth. Appl. 71(12), e999–e1004 (2009)) which is based on a reduction to finite horizon and on a work in the finite-horizon setting due to Arkin and Evstigneev.

References

  1. 8.
    J. Blot, Infinite-Horizon Problems Under Holonomic Constraints, Lecture Notes in Economics and Mathematical Systems, vol. 429 (Springer, Berlin, 1995) pp. 46–59Google Scholar
  2. 10.
    J. Blot, An infinite-horizon stochastic discrete-time Pontryagin principle, Nonlinear Anal.: Theor. Meth. Appl. 71(12), e999–e1004 (2009)Google Scholar
  3. 14.
    J. Blot, P. Cartigny, Bounded solutions and oscillations of convex Lagrangian systems in presence of a discount rate, Zeitschrift für Analysis und ihre Anwendungen 14(4), 731–750 (1995)MathSciNetCrossRefMATHGoogle Scholar
  4. 15.
    J. Blot, P. Cartigny, Optimality in infinite-horizon problems under signs conditions, J. Optim. Theor. Appl. 106(2), 411–419 (2000)MathSciNetCrossRefMATHGoogle Scholar
  5. 17.
    J. Blot, B. Crettez, On the smoothness of optimal paths, Decis. Econ. Finance 27, 1–34 (2004)MathSciNetCrossRefMATHGoogle Scholar
  6. 18.
    J. Blot, B. Crettez, On the smoothness of optimal paths II: some local turnpike results, Decis. Econ. Finance 30(2), 137–180 (2007)MathSciNetCrossRefMATHGoogle Scholar
  7. 20.
    J. Blot, N. Hayek, Second-order necessary conditions for the infinite-horizon variational problems, Math. Oper. Res. 21(4), 979–990 (1996)MathSciNetCrossRefMATHGoogle Scholar
  8. 21.
    J. Blot, N. Hayek, Sufficient conditions for the infinite-horizon variational problems, Esaim-COCV 5, 279–1292 (2000)MathSciNetCrossRefMATHGoogle Scholar
  9. 22.
    J. Blot, N. Hayek, Conjugate points in infinite-horizon optimal control problems, Automatica 37, 523–526 (2001)MathSciNetCrossRefMATHGoogle Scholar
  10. 27.
    J. Blot, P. Michel, First-order necessary conditions for the infinite-horizon variational problems, J. Optim. Theor. Appl. 88(2), 339–364 (1996)MathSciNetCrossRefMATHGoogle Scholar
  11. 28.
    J. Blot, P. Michel, The value-function of an infinite-horizon linear-quadratic problem, Appl. Math. Lett. 16, 71–78 (2003)MathSciNetCrossRefMATHGoogle Scholar
  12. 34.
    D.A. Carlson, A.B. Haurie, A. Leizarowitz, Infinite Horizon Optimal Control; Deterministic and Stochastic Systems, 2nd, revised and enlarged edn. (Springer, Berlin, 1991)Google Scholar
  13. 68.
    L.W. McKenzie, Optimal Economic Growth, turnpike Theorems and Comparative Dynamics, ed. by K.J. Arroxw, M.D. Intriligator. Handbook of Mathematical Economics, volume III, (North-Holland, Amsterdam, 1986) pp. 1281–1355Google Scholar
  14. 72.
    P. Michel, Some clarifications on the transversality conditions, Econometrica 58(3), 705–728 (1990)MathSciNetCrossRefMATHGoogle Scholar
  15. 94.
    A.J. Zaslavski, Turnpike Properties in the Calculus of Variations and Optimal Control (Springer Science + Business Media, New York, NY, 2006)MATHGoogle Scholar

Copyright information

© Joël Blot, Naïla Hayek 2014

Authors and Affiliations

  • Joël Blot
    • 1
  • Naïla Hayek
    • 2
  1. 1.Université Paris 1 Panthéon-SorbonneParisFrance
  2. 2.Université Paris 2 Panthéon-AssasParisFrance

Personalised recommendations