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Optimal discounted control for a continuous time inventory model

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Abstract

This paper is concerned with the following linear stochastic control problem: Minimize the discounted total cost

$$J(x; u) = E{_x} \left[ {\int_0^\infty {\exp [ - \alpha t]\{ \phi (x{_t} ) + |u{_t} |\} } dt} \right]$$

over all measurable and nonanticipative control processes (u t ), subject todx t =u t dt+dw t ,x(0)=x, |u t |≤1. This problem is analyzed using a discretization technique. The results obtained extend those derived in Ref. 1 and some of those derived in Ref. 2.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Bonn, Bonn, West Germany

    K. Helmes (Assistant Professor)

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  1. K. Helmes
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Additional information

Communicated by R. Rishel

This work is dedicated to Prof. Dr. W. Vogel on the occasion of his sixtieth birthday.

This work was supported by the Deutsche Forschungsgemeinschaft (DFG), Sonder-forschungsbereich 72 (SFB 72), at the University of Bonn, Bonn, West Germany.

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Helmes, K. Optimal discounted control for a continuous time inventory model. J Optim Theory Appl 44, 75–94 (1984). https://doi.org/10.1007/BF00934895

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