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

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Author Info

  • 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)

Abstract

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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Bibliographic Info

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

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Related research

Keywords: stochastic irreversible investment; optimal stopping; the Bank and El Karoui Representation Theorem; base capacity; Lagrange multiplier optional measure;

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References

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  1. Peter Bank & Frank Riedel, 2003. "Optimal Dynamic Choice of Durable and Perishable Goods," Bonn Econ Discussion Papers bgse29_2003, University of Bonn, Germany.
  2. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
  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.
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Cited by:
  1. Giorgio Ferrari & Jan-Henrik Steg & Frank Riedel, 2013. "Continuous-Time Public Good Contribution under Uncertainty," Working Papers 485, Bielefeld University, Center for Mathematical Economics.

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