On Irreversible Investment

45 Pages Posted: 15 Jul 2006

See all articles by Frank Riedel

Frank Riedel

Bielefeld University - Center for Mathematical Economics

Xia Su

University of Bonn - Economic Science Area

Date Written: June 3, 2006

Abstract

This paper develops a general theory of irreversible investment of a single firm that chooses a dynamic capacity expansion plan in an uncertain environment. The model is set up free of any distributional or any parametric assumptions and hence encompasses all the existing models. As the first contribution, a general existence and uniqueness result is provided for the optimal investment policy. Based upon an alternative approach developed previously to dynamic programming problems, we derive the optimal base capacity policy such that the firm always keeps the capacity at or above the base capacity. The critical base capacity is explicitly constructed and characterized via a stochastic backward equation. This method allows qualitative insights into the nature of the optimal investment under irreversibility. Finally, explicit solutions are derived for infinite time horizon, a separable operating profit function of Cobb--Douglas type and an exponential Levy process modelled economic shock.

Keywords: Irreversible Investment, Capacity Expansion, Singular Control Problem, Levy Processes

JEL Classification: C61, D81, E22, G11

Suggested Citation

Riedel, Frank and Su, Xia, On Irreversible Investment (June 3, 2006). Available at SSRN: https://ssrn.com/abstract=914575 or http://dx.doi.org/10.2139/ssrn.914575

Frank Riedel

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Xia Su (Contact Author)

University of Bonn - Economic Science Area ( email )

Adenauerallee 24-42
D-53113 Bonn
Germany

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