Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources
AbstractIn 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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Bibliographic InfoPaper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 463.
Length: 26 pages
Date of creation: Mar 2012
Date of revision:
stochastic irreversible investment; optimal stopping; the Bank and El Karoui Representation Theorem; base capacity; Lagrange multiplier optional measure;
Other versions of this item:
- Maria B. Chiarolla & Giorgio Ferrari & Frank Riedel, 2012. "Generalized Kuhn-Tucker Conditions for N-Firm Stochastic Irreversible Investment under Limited Resources," Papers 1203.3757, arXiv.org, revised Aug 2013.
- C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
- E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Capital; Investment; Capacity
- D92 - Microeconomics - - Intertemporal Choice - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
- G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies
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