Finance: MFG model with a long-lived penalty at random jump times
Published: 13 January 2022
26 January. Dr Clémence Alasseur, EDF Group
Dr Clémence Alasseur, EDF Group
'MFG model with a long-lived penalty at random jump times' joint paper with Luciano Campi, Roxana Dumitrescu, Jia Zeng.
Wednesday 26 January, 1pm - 2.15pm
Zoom online seminar
Abstract
We consider an energy system with n consumers who are linked by a Demand Side Management (DSM) contract, i.e. they agreed to diminish, at random times, their aggregated power consumption by a predefined volume during a predefined duration. Their failure to deliver the service is penalised via the difference between the sum of the n power consumptions and the contracted target. We are led to analyse a non-zero sum stochastic game with n players, where the interaction takes place through a cost which involves a delay induced by the duration included in the DSM contract. When n→∞, we obtain a Mean-Field Game (MFG) with random jump time penalty and interaction on the control. We prove a stochastic maximum principle in this context, which allows to compare the MFG solution to the optimal strategy of a central planner. In a linear quadratic setting we obtain an semi-explicit solution through a system of decoupled forward-backward stochastic differential equations with jumps, involving a Riccati Backward SDE with jumps. We show that it provides an approximate Nash equilibrium for the original n-player game for n large. Finally, we propose a numerical algorithm to compute the MFG equilibrium and present several numerical experiments. This is a joint work with Luciano Campi, Roxana Dumitrescu and Jia Zeng.
Biography
Dr Clémence Alasseur is currently the Head of EDF R&D team - Energy and Financial Markets, Risks and Valuation. From 2014 to 2021 she was Director of the Finance of Energy Markets laboratory (www.fime-lab.org). Previously, she directed R&D projects on energy market risk management with business divisions of EDF Group. Her research interests include the modeling of power prices, finance and incentive theory applied to the electricity system.
Further information: business-events@glasgow.ac.uk
First published: 13 January 2022
<< 2022