Journal of Optimization Theory and Applications

, Volume 44, Issue 1, pp 75–94 | Cite as

Optimal discounted control for a continuous time inventory model

  • K. Helmes
Contributed Papers


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.

Key Words

Discounted stochastic control controlled Markov chains approximation of controlled diffusions Bellman equation Bellman's optimality principle 


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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • K. Helmes
    • 1
  1. 1.Institut für Angewandte MathematikUniversität BonnBonnWest Germany

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