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A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis

  • Tiziano De Angelis

    (University of Manchester)

  • Giorgio Ferrari

    (Bielefeld University)

We study a continuous-time, finite horizon optimal stochastic reversible investment problem for a firm producing a single good. The production capacity is modeled as a one-dimensional, time-homogeneous, linear diffusion controlled by a bounded variation process which represents the cumulative investment-disinvestment strategy. We associate to the investmentdisinvestment problem a zero-sum optimal stopping game and characterize its value function through a free boundary problem with two moving boundaries. These are continuous, bounded and monotone curves that solve a system of non-linear integral equations of Volterra type. The optimal investment-disinvestment strategy is then shown to be a diffusion reflected at the two boundaries.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-477.pdf
File Function: First version, 2013
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Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 477.

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Length: 42 pages
Date of creation: Apr 2013
Date of revision:
Handle: RePEc:bie:wpaper:477
Contact details of provider: Postal: Postfach 10 01 31, 33501 Bielefeld
Phone: +49(0)521-106-4907
Web page: http://www.imw.uni-bielefeld.de/

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  1. Goran Peskir, 2005. "The Russian option: Finite horizon," Finance and Stochastics, Springer, vol. 9(2), pages 251-267, 04.
  2. Maria B. Chiarolla & Giorgio Ferrari & Frank Riedel, 2012. "Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources," Papers 1203.3757, arXiv.org, revised Aug 2013.
  3. Abel, Andrew B & Eberly, Janice C, 1996. "Optimal Investment with Costly Reversibility," Review of Economic Studies, Wiley Blackwell, vol. 63(4), pages 581-93, October.
  4. 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.
  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. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
  7. Anders ├╗ksendal, 2000. "Irreversible investment problems," Finance and Stochastics, Springer, vol. 4(2), pages 223-250.
  8. Xia Su & Frank Riedel, 2006. "On Irreversible Investment," Bonn Econ Discussion Papers bgse13_2006, University of Bonn, Germany.
  9. Bentolila, Samuel & Bertola, Giuseppe, 1990. "Firing Costs and Labour Demand: How Bad Is Eurosclerosis?," Review of Economic Studies, Wiley Blackwell, vol. 57(3), pages 381-402, July.
  10. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
  11. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
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