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Roxana Dumitrescu (King’s College de Londres) “Energy transition: a mean-field game approach”

April 11 @ 3:15 pm - 4:15 pm

Finance & Financial Econometrics : 
Time: 15.15 pm – 16.15 pm
Date: 11th of April 2023
Room 3001

Roxana Dumitrescu (King’s College de Londres) “Energy transition: a mean-field game approach”

Abstract :

In this talk, I will discuss two models developed in the context of energy transition – from both supply and demand sides – using as a mathematical tool the theory on mean-field games. I will first present a model for the industry dynamics in the electricity market, based on mean-field games of optimal stopping. In this model, there are two types of agents: the renewable producers and the conventional producers. The renewable producers choose the optimal moment to build new renewable plants, and the conventional producers choose the optimal moment to exit the market. The agents interact through the market price, determined by matching the aggregate supply of the two types of producers with an exogenous demand function. Using a relaxed formulation of optimal stopping mean-field games, we prove the existence of a Nash equilibrium and the uniqueness of the equilibrium price process. An empirical example, inspired by the UK electricity market, is presented.

In the second part of the talk, we focus on demand-side strategies to deal with the increase of intermittant renewable energy. 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. The asymptotic formulation can be written in terms of Mean-Field Game (MFG) with random jump time penalty and interaction on the control. We prove the existence of an equilibria, which admits a semi-explicit representation in the linear-quadratic case, and present several numerical illustrations.

The first part is based on a joint work with R. Aid (Univ. Dauphine) and P. Tankov (Ensae), and the second part on a joint work with C. Alasseur (EDF), L. Campi (Univ of Milan) and J. Zeng (King’s College).