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

Arbeitspapier

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)].

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Working Papers ; No. 463

Classification and Topics

• Classification: Wirtschaft ; Mathematical Methods ; Investment; Capital; Intangible Capital; Capacity ; Capital Budgeting; Fixed Investment and Inventory Studies; Capacity
• Subject: stochastic irreversible investment ; optimal stopping ; the Bank and El Karoui Representation Theorem ; base capacity ; Lagrange multiplier optional measure ; Investition ; Sunk Costs ; Stochastischer Prozess ; Suchtheorie ; Nichtlineare Optimierung ; Theorie

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Chiarolla, Maria B. ; Ferrari, Giorgio ; Riedel, Frank
• Event: Veröffentlichung
• (who): Bielefeld University, Institute of Mathematical Economics (IMW)
• (where): Bielefeld
• (when): 2012

Further information

• Handle: http://hdl.handle.net/10419/81114
• URN: urn:nbn:de:0070-pub-26717275
• Last update: 10.03.2025, 11:42 AM CET