TY  - GEN
AB  - 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].
DA  - 2012
KW  - base capacity
KW  - Lagrange multiplier optional measure
KW  - stochastic irreversible investment
KW  - the Bank and El KarouiRepresentation Theorem
KW  - optimal stopping
LA  - eng
PY  - 2012
SN  - 0931-6558
SP  - 25-
TI  - Generalized Kuhn–Tucker conditions for N-Firm stochastic irreversible investment under limited resources
UR  - https://nbn-resolving.org/urn:nbn:de:0070-pub-26717275
Y2  - 2024-11-22T07:56:24
ER  -