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Optimal partially reversible investment with entry decision and general production function

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  • Guo, Xin
  • Pham, Huyên

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.

Suggested Citation

  • Guo, Xin & Pham, Huyên, 2005. "Optimal partially reversible investment with entry decision and general production function," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 705-736, May.
  • Handle: RePEc:eee:spapps:v:115:y:2005:i:5:p:705-736
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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.
    2. Anders ûksendal, 2000. "Irreversible investment problems," Finance and Stochastics, Springer, vol. 4(2), pages 223-250.
    3. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
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    Citations

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    Cited by:

    1. de Angelis, Tiziano & Federico, Salvatore & Ferrari, Giorgio, 2016. "On the Optimal Boundary of a Three-Dimensional Singular Stochastic Control Problem Arising in Irreversible Investment," Center for Mathematical Economics Working Papers 509, Center for Mathematical Economics, Bielefeld University.
    2. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," Stochastic Processes and their Applications, Elsevier, vol. 125(7), pages 2727-2751.
    3. Jean-Paul Décamps & Stéphane Villeneuve, 2007. "Optimal dividend policy and growth option," Finance and Stochastics, Springer, vol. 11(1), pages 3-27, January.
    4. repec:eee:jbfina:v:81:y:2017:i:c:p:172-180 is not listed on IDEAS
    5. De Angelis, Tiziano & Ferrari, Giorgio, 2014. "A stochastic partially reversible investment problem on a finite time-horizon: Free-boundary analysis," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4080-4119.
    6. Di Corato, Luca & Moretto, Michele & Vergalli, Sergio, 2014. "Long-run investment under uncertain demand," Economic Modelling, Elsevier, vol. 41(C), pages 80-89.
    7. Baurdoux, Erik J. & Yamazaki, Kazutoshi, 2015. "Optimality of doubly reflected Lévy processes in singular control," LSE Research Online Documents on Economics 61617, London School of Economics and Political Science, LSE Library.
    8. Joachim Gahungu and Yves Smeers, 2012. "A Real Options Model for Electricity Capacity Expansion," RSCAS Working Papers 2012/08, European University Institute.
    9. Salvatore Federico & Mauro Rosestolato & Elisa Tacconi, 2018. "Irreversible investment with fixed adjustment costs: a stochastic impulse control approach," Papers 1801.04491, arXiv.org.
    10. 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.
    11. de Angelis, Tiziano & Ferrari, Giorgio, 2016. "Stochastic nonzero-sum games: a new connection between singular control and optimal stopping," Center for Mathematical Economics Working Papers 565, Center for Mathematical Economics, Bielefeld University.
    12. Tiziano De Angelis & Salvatore Federico & Giorgio Ferrari, 2014. "Optimal Boundary Surface for Irreversible Investment with Stochastic Costs," Papers 1406.4297, arXiv.org, revised Jan 2017.
    13. repec:spr:compst:v:76:y:2012:i:3:p:239-271 is not listed on IDEAS
    14. Xin Guo & Pascal Tomecek, 2008. "Solving Singular Control from Optimal Switching," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(1), pages 25-45, March.
    15. de Angelis, Tiziano & Ferrari, Giorgio & Martyr, Randall & Moriarty, John, 2016. "Optimal entry to an irreversible investment plan with non convex costs," Center for Mathematical Economics Working Papers 566, Center for Mathematical Economics, Bielefeld University.
    16. Pekka Matomäki, 2012. "On solvability of a two-sided singular control problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 239-271, December.
    17. Yiannis Kamarianakis & Anastasios Xepapadeas, 2007. "An Irreversible Investment Model with a Stochastic Production Capacity and Fixed Plus Proportional Adjustment Costs," Working Papers 0708, University of Crete, Department of Economics.
    18. Johnson, Timothy C. & Zervos, Mihail, 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.
    19. Giorgio Ferrari & Tiziano Vargiolu, 2017. "On the Singular Control of Exchange Rates," Papers 1712.02164, arXiv.org.

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