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On the Lack of Optimal Classical Stochastic Controls in a Capacity Expansion Problem

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  • Maria B. Chiarolla

Abstract

The stochastic control problem of a firm aiming to optimally expand the production capacity, through irreversible investment, in order to maximize the expected total profits on a finite time interval has been widely studied in the literature when the firm’s capacity is modeled as a controlled Itˆo process in which the control enters additively and it is a general nondecreasing stochastic process, possibly singular as a function of time, representing the cumulative investment up to time t. This note proves that there is no solution when the problems falls in the so-called classical control setting; that is, when the control enters the capacity process as the rate of real investment, and hence the cumulative investment up to time t is an absolutely continuous process (as a function of time). So, in a sense, this note explains the need for the larger class of nondecreasing control processes appearing in the literature.

Suggested Citation

  • Maria B. Chiarolla, 2019. "On the Lack of Optimal Classical Stochastic Controls in a Capacity Expansion Problem," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 11(6), pages 1-89, December.
    • Handle: RePEc:ibn:jmrjnl:v:11:y:2019:i:6:p:89
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    References listed on IDEAS

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    1. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
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    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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