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

Chiarolla MB, Ferrari G, Riedel F (2012) Working Papers. Institute of Mathematical Economics; 463.
Bielefeld: Center for Mathematical Economics.

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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].
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Chiarolla MB, Ferrari G, Riedel F. Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources. Working Papers. Institute of Mathematical Economics. Vol 463. Bielefeld: Center for Mathematical Economics; 2012.
Chiarolla, M. B., Ferrari, G., & Riedel, F. (2012). Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources (Working Papers. Institute of Mathematical Economics, 463). Bielefeld: Center for Mathematical Economics.
Chiarolla, M. B., Ferrari, G., and Riedel, F. (2012). Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources. Working Papers. Institute of Mathematical Economics, 463, Bielefeld: Center for Mathematical Economics.
Chiarolla, M.B., Ferrari, G., & Riedel, F., 2012. Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources, Working Papers. Institute of Mathematical Economics, no.463, Bielefeld: Center for Mathematical Economics.
M.B. Chiarolla, G. Ferrari, and F. Riedel, Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources, Working Papers. Institute of Mathematical Economics, vol. 463, Bielefeld: Center for Mathematical Economics, 2012.
Chiarolla, M.B., Ferrari, G., Riedel, F.: Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources. Working Papers. Institute of Mathematical Economics, 463. Center for Mathematical Economics, Bielefeld (2012).
Chiarolla, Maria B., Ferrari, Giorgio, and Riedel, Frank. Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources. Bielefeld: Center for Mathematical Economics, 2012. Working Papers. Institute of Mathematical Economics. 463.
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