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A Model For The Long-Term Optimal Capacity Level Of An Investment Project

Author

Listed:
  • ARNE LØKKA

    (Department of Mathematics, Columbia House, London School of Economics, Houghton Street, London WC2A 2AE, UK)

  • MIHAIL ZERVOS

    (Department of Mathematics, Columbia House, London School of Economics, Houghton Street, London WC2A 2AE, UK)

Abstract

We consider an investment project that produces a single commodity. The project's operation yields payoff at a rate that depends on the project's installed capacity level and on an underlying economic indicator such as the output commodity's price or demand, which we model by an ergodic, one-dimensional Itô diffusion. The project's capacity level can be increased dynamically over time. The objective is to determine a capacity expansion strategy that maximizes the ergodic or long-term average payoff resulting from the project's management. We prove that it is optimal to increase the project's capacity level to a certain value and then take no further actions. The optimal capacity level depends on both the long-term average and the volatility of the underlying diffusion.

Suggested Citation

  • Arne Løkka & Mihail Zervos, 2011. "A Model For The Long-Term Optimal Capacity Level Of An Investment Project," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(02), pages 187-196.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:02:n:s0219024911006322
    DOI: 10.1142/S0219024911006322
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    Cited by:

    1. Ferrari, Giorgio & Li, Hanwu & Riedel, Frank, 2020. "A Knightian Irreversible Investment Problem," Center for Mathematical Economics Working Papers 634, Center for Mathematical Economics, Bielefeld University.
    2. Laruelle Sophie & Pagès Gilles, 2012. "Stochastic approximation with averaging innovation applied to Finance," Monte Carlo Methods and Applications, De Gruyter, vol. 18(1), pages 1-51, January.
    3. Andrea Bovo & Tiziano De Angelis & Jan Palczewski, 2023. "Zero-sum stopper vs. singular-controller games with constrained control directions," Papers 2306.05113, arXiv.org, revised Feb 2024.
    4. Andrea Bovo & Tiziano De Angelis & Jan Palczewski, 2023. "Stopper vs. singular-controller games with degenerate diffusions," Papers 2312.00613, arXiv.org, revised Jul 2024.
    5. Duy Nguyen & Jingzhi Tie & Qing Zhang, 2014. "An Optimal Trading Rule Under a Switchable Mean-Reversion Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 145-163, April.

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