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Additional exercises for Part IV

  • Francis Clarke
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 264)

Abstract

This chapter consists of a collection of exercises on optimal control, the first of which is the following: Optimal control problems which arise in economics or finance often feature a discount rate δ. This parameter is used to express the present value of future revenues or expenses. We introduce this consideration in the problem described on p. 445, by modifying the cost functional (but nothing else) as follows:
$$J(x ,u)\: = \:\int_{ 0}^{\,T} e^{-\delta t}\big(\, x(t)+u(t)\big)\, dt\,. $$
For small δ>0, it can be shown that the optimal process has the same general turnpike nature as before, but with a different turnpike value (depending on δ) for the state. Determine that value.

Keywords

Functional Analysis Control Problem System Theory Optimal Process Discount Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [13]
    F. H. Clarke. Optimization and Nonsmooth Analysis. Wiley-Interscience, New York, 1983. Republished as vol. 5 of Classics in Applied Mathematics, SIAM, 1990. Google Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Francis Clarke
    • 1
  1. 1.Institut Camille JordanUniversité Claude Bernard Lyon 1VilleurbanneFrance

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