An irreversible investment problem with maintenance expenditure on a finite horizon: Free boundary analysis

This paper concerns a continuous-time, finite horizon, optimal irreversible investment problem with maintenance expenditure of a firm under uncertainty. We assume that the firm can make irreversible investments to expand its production capacity and spend maintenance expenditure to achieve better per...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 440; no. 2; pp. 597 - 623
Main Authors: Han, Xiaoru, Yi, Fahuai
Format: Journal Article
Language:English
Published: Elsevier Inc 15.08.2016
Subjects:
Finite horizon
Free boundary problem
Irreversible investment
Maintenance
Singular stochastic control
Variational inequality
Finite horizon
Irreversible investment
Maintenance
Free boundary problem
Variational inequality
Singular stochastic control
ISSN:0022-247X, 1096-0813
Online Access:Get full text
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Summary:This paper concerns a continuous-time, finite horizon, optimal irreversible investment problem with maintenance expenditure of a firm under uncertainty. We assume that the firm can make irreversible investments to expand its production capacity and spend maintenance expenditure to achieve better performance of the productivity. The objective of the firm is to construct optimal investment and maintenance policies to maximize its expected total profit over a finite horizon. Mathematically, it is a singular stochastic control problem whose value function satisfies a parabolic variational inequality with gradient constraint. The problem gives rise to two free boundaries which stand for the optimal investment and maintenance strategies, respectively. We investigate behaviors of free boundaries, study regularities of the value function, and give optimal investment and maintenance policies. As we know, this is a first integral result for an investment–maintenance problem with a finite time horizon due to use of partial differential equation (PDE) technique.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2016.03.048