De Angelis, T, Federico, S and Ferrari, G (2017) Optimal Boundary Surface for Irreversible Investment with Stochastic Costs. Mathematics of Operations Research, 42 (4). pp. 1135-1161. ISSN 0364-765X
Abstract
This paper examines a Markovian model for the optimal irreversible investment problem of a rm aiming at minimizing total expected costs of production. We model market uncertainty and the cost of investment per unit of production capacity as two independent one-dimensional regular di usions, and we consider a general convex running cost function. The optimization problem is set as a three-dimensional degenerate singular stochastic control problem. We provide the optimal control as the solution of a reflected diffusion at a suitable boundary surface. Such boundary arises from the analysis of a family of two-dimensional parameter-dependent optimal stopping problems and it is characterized in terms of the family of unique continuous solutions to parameter-dependent nonlinear integral equations of Fredholm type.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017, INFORMS. This is an author produced version of a paper published in Mathematics of Operations Research. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Irreversible investment; singular stochastic control; optimal stopping; free-boundary problems; nonlinear integral equations |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 31 Oct 2016 13:04 |
Last Modified: | 16 May 2018 00:38 |
Status: | Published |
Publisher: | INFORMS |
Identification Number: | 10.1287/moor.2016.0841 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:106696 |