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

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  • Tiziano De Angelis

    (University of Manchester)

  • Giorgio Ferrari

    (Bielefeld University)

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    Abstract

    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/n/upload/paper/be83ab3ecd0db773eb2dc1b0a17836a1.pdf
    File Function: First version, 2013
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    Bibliographic Info

    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

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    Related research

    Keywords: reversible investment; singular stochastic control; zero-sum optimal stopping games; free boundary problems; Skorokhod reflection problem;

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    References

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    1. 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.
    2. Anders ├╗ksendal, 2000. "Irreversible investment problems," Finance and Stochastics, Springer, vol. 4(2), pages 223-250.
    3. Frank Riedel & Xia Su, 2011. "On irreversible investment," Finance and Stochastics, Springer, vol. 15(4), pages 607-633, December.
    4. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
    5. Goran Peskir, 2005. "The Russian option: Finite horizon," Finance and Stochastics, Springer, vol. 9(2), pages 251-267, 04.
    6. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
    7. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
    8. 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.
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