Energy transition under scenario uncertainty: a mean-field game of stopping with common noise

We study the impact of transition scenario uncertainty, namely that of future carbon price and electricity demand, on the pace of decarbonization of the electricity industry. To this end, we develop a theory of optimal stopping mean-field games with non-Markovian common noise and partial observation...

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Bibliographic Details
Published inMathematics and financial economics Vol. 18; no. 2-3; pp. 233 - 274
Main Authors Dumitrescu, Roxana, Leutscher, Marcos, Tankov, Peter
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2024
Subjects
Applications of Mathematics
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Insurance
Macroeconomics/Monetary Economics//Financial Economics
Management
Mathematics
Mathematics and Statistics
Quantitative Finance
Statistics for Business
Partial information
91A13
Mean-field games
91A55
Optimal stopping
Energy transition
Electricity market
Common noise
91A80
C73
Q42
Scenario uncertainty
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Summary:We study the impact of transition scenario uncertainty, namely that of future carbon price and electricity demand, on the pace of decarbonization of the electricity industry. To this end, we develop a theory of optimal stopping mean-field games with non-Markovian common noise and partial observation. For mathematical tractability, the theory is formulated in discrete time and with common noise restricted to a finite probability space. We prove the existence of Nash equilibria for this game using the linear programming approach. We then apply the general theory to build a discrete time model for the long-term dynamics of the electricity market subject to common random shocks affecting the carbon price and the electricity demand. We consider two classes of agents: conventional producers and renewable producers. The former choose an optimal moment to exit the market and the latter choose an optimal moment to enter the market by investing into renewable generation. The agents interact through the market price determined by a merit order mechanism with an exogenous stochastic demand. We illustrate our model by an example inspired by the UK electricity market, and show that scenario uncertainty leads to significant changes in the speed of replacement of conventional generators by renewable production.
ISSN:1862-9679
1862-9660
DOI:10.1007/s11579-023-00352-w