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Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources

  • Maria B. Chiarolla

    (Dipartimento di Metodi e Modelli per l’Economia, il Territorio e la Finanza, Università di Roma ‘La Sapienza’)

  • Giorgio Ferrari

    (Dipartimento di Metodi e Modelli per l’Economia, il Territorio e la Finanza, Università di Roma ‘La Sapienza’)

  • Frank Riedel

    ()

    (Institute of Mathematical Economics, Bielefeld University)

In this paper we study a continuous time, optimal stochastic investment problem under limited resources in a market with N firms. The investment processes are subject to a time-dependent stochastic constraint. Rather than using a dynamic programming approach, we exploit the concavity of the profit functional to derive some necessary and sufficient first order conditions for the corresponding Social Planner optimal policy. Our conditions are a stochastic infinite-dimensional generalization of the Kuhn-Tucker Theorem. As a subproduct we obtain an enlightening interpretation of the first order conditions for a single firm in Bank [SIAM Journal on Control and Optimization 44 (2005)]. In the infinite-horizon case, with operating profit functions of Cobb-Douglas type, our method allows the explicit calculation of the optimal policy in terms of the ‘base capacity’ process, i.e. the unique solution of the Bank and El Karoui representation problem [Annals of Probability 32 (2004)].

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-463.pdf
File Function: First version, 2012
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Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 463.

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Length: 26 pages
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:bie:wpaper:463
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. Peter Bank & Frank Riedel, 2003. "Optimal Dynamic Choice of Durable and Perishable Goods," Levine's Bibliography 666156000000000402, UCLA Department of Economics.
  2. Y.M. Kabanov, 1999. "Hedging and liquidation under transaction costs in currency markets," Finance and Stochastics, Springer, vol. 3(2), pages 237-248.
  3. Xia Su & Frank Riedel, 2006. "On Irreversible Investment," Bonn Econ Discussion Papers bgse13_2006, University of Bonn, Germany.
  4. 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.
  5. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
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