De Angelis, T, Ferrari, G and Moriarty, J (2019) A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Nonconvex Costs. Mathematics of Operations Research, 44 (2). pp. 512-531. ISSN 0364-765X
Abstract
In this paper we provide a complete theoretical analysis of a two-dimensional degenerate nonconvex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control, and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and the smooth fit condition holds there.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2019, INFORMS. This article is protected by copyright. All rights reserved. This is an author produced version of a paper accepted for publication in Mathematics of Operations Research. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | finite-fuel singular stochastic control; optimal stopping; free boundary; Hamilton–Jacobi–Bellman equation; irreversible investment; electricity market |
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: | 14 Feb 2018 16:19 |
Last Modified: | 17 Jun 2019 11:35 |
Status: | Published |
Publisher: | INFORMS |
Identification Number: | 10.1287/moor.2018.0934 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:127276 |