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Optimal partially reversible investment with entry decision and general production function

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  • Guo, Xin
  • Pham, Huyên
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    Abstract

    This paper studies the problem of a company that adjusts its stochastic production capacity in reversible investments with controls of expansion and contraction. The company may also decide on the activation time of its production. The profit production function is of a very general form satisfying minimal standard assumptions. The objective of the company is to find an optimal entry and production decision to maximize its expected total net profit over an infinite time horizon. The resulting dynamic programming principle is a two-step formulation of a singular stochastic control problem and an optimal stopping problem. The analysis of value functions relies on viscosity solutions of the associated Bellman variational inequations. We first state several general properties and in particular smoothness results on the value functions. We then provide a complete solution with explicit expressions of the value functions and the optimal controls: the company activates its production once a fixed entry-threshold of the capacity is reached, and invests in capital so as to maintain its capacity in a closed bounded interval. The boundaries of these regions can be computed explicitly and their behavior is studied in terms of the parameters of the model.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 115 (2005)
    Issue (Month): 5 (May)
    Pages: 705-736

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    Handle: RePEc:eee:spapps:v:115:y:2005:i:5:p:705-736

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    Related research

    Keywords: Singular stochastic control Optimal stopping Viscosity solutions Skorohod problem Reversible investment Production;

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    Cited by:
    1. Xin Guo & Pascal Tomecek, 2008. "Solving Singular Control from Optimal Switching," Asia-Pacific Financial Markets, Springer, vol. 15(1), pages 25-45, March.
    2. Pekka Matomäki, 2012. "On solvability of a two-sided singular control problem," Computational Statistics, Springer, vol. 76(3), pages 239-271, December.
    3. Hamadène, Said & Zhang, Jianfeng, 2010. "Switching problem and related system of reflected backward SDEs," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 403-426, April.
    4. Tiziano De Angelis & Salvatore Federico & Giorgio Ferrari, 2014. "On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment," Working Papers 509, Bielefeld University, Center for Mathematical Economics.
    5. Tiziano De Angelis & Salvatore Federico & Giorgio Ferrari, 2014. "On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment," Papers 1406.4297, arXiv.org.
    6. Jean-Paul Décamps & Stéphane Villeneuve, 2007. "Optimal dividend policy and growth option," Finance and Stochastics, Springer, vol. 11(1), pages 3-27, January.
    7. Joachim Gahungu and Yves Smeers, 2012. "A Real Options Model for Electricity Capacity Expansion," RSCAS Working Papers 2012/08, European University Institute.
    8. Yiannis Kamarianakis & Anastasios Xepapadeas, 2006. "An irreversible investment model with a stochastic production capacity and fixed plus proportional adjustment costs," Working Papers 0708, University of Crete, Department of Economics.
    9. Timothy C. Johnson & Mihail Zervos, 2010. "The explicit solution to a sequential switching problem with non-smooth data," LSE Research Online Documents on Economics 29003, London School of Economics and Political Science, LSE Library.

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