Short Communications

On optimization of long-term irreversible investments in a diffusion model

E. B. Boguslavskaya

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: In [J. Finan. Econ., 34 (1993), pp. 53–76] R. Pindyck introduced a model where uncertainty arises from the unknown amount of investments needed to complete a project. In this paper, we obtain an explicit solution for this problem.
To find a solution we use heuristic arguments based on the Bellman equation and the “smooth pasting condition”. To prove optimality of the solution we use verification theorems of stochastic optimal control.

Keywords: optimal control of investments, Bellman equation, smooth pasting conditions, utility function, profit function, Bessel functions, Kummer functions, hypergeometric functions.

Received: 01.10.1998

DOI: 10.4213/tvp504

 English version: Theory of Probability and its Applications, 2001, 45:4, 647–658

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