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On Irreversible Investment

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  • Xia Su
  • Frank Riedel

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Abstract

This paper develops a general theory of irreversible investment of a single firm that chooses a dynamic capacity expansion plan in an uncertain environment. The model is set up free of any distributional or any parametric assumptions and hence encompasses all the existing models. As the first contribution, a general existence and uniqueness result is provided for the optimal investment policy. Based upon an alternative approach developed previously to dynamic programming problems, we derive the optimal base capacity policy such that the firm always keeps the capacity at or above the base capacity. The critical base capacity is explicitly constructed and characterized via a stochastic backward equation. This method allows qualitative insights into the nature of the optimal investment under irreversibility. It is demonstrated that the marginal profit is indeed equal to the user cost of capital in free intervals where investment occurs in an absolutely continuous way at strictly positive rates. However, the equality is maintained only in expectation on average in blocked intervals where no investment occurs. Whenever the uncertainty is generated by a diffusion, the investment is singular with respect to Lebesgue measure. In contrast to the deterministic and Brownian motion case where lump sum investment takes place only at time zero, the firm responses in general more frequently in jumps to shocks. Nevertheless, lump sum investments are shown to be possible only at information surprises which is defined as unpredictable stopping time or unanticipated information jump even at the predictable time. Furthermore, general monotone comparative statics results are derived for the relevant ingredients of the model. Finally, explicit solutions are derived for infinite time horizon, a separable operating profit function of Cobb--Douglas type and an exponential Levy process modelled economic shock.

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File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse13_2006.pdf
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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse13_2006.

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Length: 45
Date of creation: Jun 2006
Date of revision:
Handle: RePEc:bon:bonedp:bgse13_2006

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

Related research

Keywords: Sequential Irreversible Investment; Capacity Expansion; Singular Control Problem; Levy Processes;

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References

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Citations

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Cited by:
  1. Maria B. Chiarolla & Giorgio Ferrari & Frank Riedel, 2012. "Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources," Working Papers 463, Bielefeld University, Center for Mathematical Economics.
  2. Giorgio Ferrari, 2012. "On an Integral Equation for the Free Boundary of Stochastic, Irreversible Investment Problems," Working Papers 471, Bielefeld University, Center for Mathematical Economics.
  3. Giorgio Ferrari, 2012. "On an Integral Equation for the Free-Boundary of Stochastic, Irreversible Investment Problems," Papers 1211.0412, arXiv.org, revised Jul 2013.
  4. Jan-Henrik Steg, 2012. "Irreversible investment in oligopoly," Finance and Stochastics, Springer, vol. 16(2), pages 207-224, April.
  5. Maria B. Chiarolla & Giorgio Ferrari, 2011. "Identifying the Free Boundary of a Stochastic, Irreversible Investment Problem via the Bank-El Karoui Representation Theorem," Papers 1108.4886, arXiv.org, revised Dec 2013.
  6. Giorgio Ferrari & Jan-Henrik Steg & Frank Riedel, 2013. "Continuous-Time Public Good Contribution under Uncertainty," Working Papers 485, Bielefeld University, Center for Mathematical Economics.
  7. Tiziano De Angelis & Giorgio Ferrari, 2013. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Working Papers 477, Bielefeld University, Center for Mathematical Economics.
  8. Francisco Ruiz-Aliseda & Jianjun Wu, 2007. "Irreversible investment in stochastically cyclical markets," Economics Working Papers 1018, Department of Economics and Business, Universitat Pompeu Fabra.
  9. 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.
  10. 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.

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