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System Modelling and Optimization pp 424–432Cite as

Some singular control problem with long term average criterion

  • Stochastic Control
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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 59))

Abstract

in this paper we consider an optimal control problem for a diffusion process y(t)=y vx solution of dy(t)=g(y)dt + σ(y)dwt+dvt, where vt is an increasing positive adapted process, with the long term average cost

$$J\left( v \right) = \mathop {\lim }\limits_{T \uparrow \infty } \inf \frac{1}{T}E\smallint _0^T f\left( {y_x^v \left( t \right)} \right)dt.$$

The paper gives, for one dimensional processes, existence result for an optimal control in relation with a reflected diffusion process as in Karatzas [16], and characterization of the optimal cost. Moreover, the asymptotic analysis of the discounted cost problem is carried out.

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Author information

Authors and Affiliations

  1. Departments of Mathematics, Wayne State University, 48202, Detroit, Michigan, U.S.A.

    J. L. Menaldi

  2. INRIA — Domaine de Voluceau Rocquencourt, B.P. 105, 78153, Le Chesnay Cedex, France

    M. Robin

Authors
  1. J. L. Menaldi
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  2. M. Robin
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P. Thoft-Christensen

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© 1984 Springer-Verlag

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Menaldi, J.L., Robin, M. (1984). Some singular control problem with long term average criterion. In: Thoft-Christensen, P. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 59. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008916

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  • DOI: https://doi.org/10.1007/BFb0008916

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13185-4

  • Online ISBN: 978-3-540-38828-9

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