Mean-field moral hazard for optimal energy demand response management
File(s)
Accepted version
Author(s)
Elie, Romuald
Hubert, Emma
Mastrolia, Thibaut
Possamaï, Dylan
Type
Journal Article
Abstract
We study the problem of demand response contracts in electricity markets by quantifying the impact of considering a continuum of consumers with mean–field interaction, whose consumption is impacted by a common noise. We formulate the problem as a Principal–Agent problem with moral hazard in which the Principal—she—is an electricity producer who observes continuously the consumption of a continuum of risk‐averse consumers, and designs contracts in order to reduce her production costs. More precisely, the producer incentivizes each consumer to reduce the average and the volatility of his consumption in different usages, without observing the efforts he makes. We prove that the producer can benefit from considering the continuum of consumers by indexing contracts on the consumption of one Agent and aggregate consumption statistics from the distribution of the entire population of consumers. In the case of linear energy valuation, we provide closed‐form expression for this new type of optimal contracts that maximizes the utility of the producer. In most cases, we show that this new type of contracts allows the Principal to choose the risks she wants to bear, and to reduce the problem at hand to an uncorrelated one.
Date Issued
2021-01
Date Acceptance
2020-09-17
Citation
Mathematical Finance, 2021, 31 (1), pp.399-473
ISSN
0960-1627
Publisher
Wiley
Start Page
399
End Page
473
Journal / Book Title
Mathematical Finance
Volume
31
Issue
1
Copyright Statement
© 2020 Wiley Periodicals LLC. This is the peer reviewed version of the following article, which has been published in final form at https://onlinelibrary.wiley.com/doi/full/10.1111/mafi.12291. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
Identifier
https://onlinelibrary.wiley.com/doi/10.1111/mafi.12291
Subjects
Finance
0102 Applied Mathematics
1502 Banking, Finance and Investment
Publication Status
Published
Date Publish Online
2020-10-13