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Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources

Maria B. Chiarolla, Giorgio Ferrari () and Frank Riedel ()
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Maria B. Chiarolla: Center for Mathematical Economics, Bielefeld University

No 463, Center for Mathematical Economics Working Papers from Center for 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 [5]. 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 [4].

Keywords: base capacity; Lagrange multiplier optional measure; stochastic irreversible investment; the Bank and El KarouiRepresentation Theorem; optimal stopping (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ore
Date: 2014-04-15
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https://pub.uni-bielefeld.de/download/2671727/2671728 First Version, 2012 (application/pdf)

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Working Paper: Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources (2013) Downloads
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