Please use this identifier to cite or link to this item:
Chiarolla, Maria B.
Ferrari, Giorgio
Riedel, Frank
Year of Publication: 
Series/Report no.: 
Working Papers, Institute of Mathematical Economics 463
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)].
stochastic irreversible investment
optimal stopping
the Bank and El Karoui Representation Theorem
base capacity
Lagrange multiplier optional measure
Document Type: 
Working Paper

Files in This Item:
431.92 kB

Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.