Details

Autor(en) / Beteiligte

• Alasseur, Clémence
• Campi, Luciano
• Dumitrescu, Roxana
• Zeng, Jia

Titel

MFG model with a long-lived penalty at random jump times: application to demand side management for electricity contracts

Ist Teil von

• Annals of operations research, 2024-05, Vol.336 (1-2), p.541-569

Ort / Verlag

New York: Springer US

Erscheinungsjahr

2024

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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 a 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.