Price Formation and Optimal Trading in Intraday Electricity Markets

Abstract

We study price formation in intraday electricity markets in the presence of intermittent renewable generation. We consider the setting where a major producer may interact strategically with a large number of small producers. Using stochastic control theory we identify the optimal strategies of agents with market impact and exhibit the Nash equilibrium in closed form in the asymptotic framework of mean field games with a major player. This is a companion paper to [12], where a similar model is developed in the setting of identical agents.

A Finite Agent Equilibrium in an Incomplete Market and its Strong Convergence to the Mean-Field Limit

“…Another approach is to impose the market clearing condition but the demand of the asset is assumed to be given by an exogenous function of price without considering the optimization problem among the agents. See [1,9,14,15,16,23,39,12,13] as interesting applications to, optimal trading, optimal liquidation, optimal oil production, and price formation in electricity markets etc., using the phenomenological approaches explained above. A notable exception directly dealing with the market clearing equilibrium is [22], where the market price process becomes deterministic due to the absence of the common noise.…”

Extended mean field control problem: a propagation of chaos result

“…Pham and Wei [32] (without common noise, with closed loop controls) and Djete, Possamaï, and Tan [10] establish the Dynamic Programming Principle (DPP for short) and give a Hamilton-Jacobi equation on a space of probability measures verified by the value function (heuristically proved in [10]). Let us also mention Carmona and Lacker [6], Elie, Mastrolia, and Possamaï [13], Cardaliaguet and Lehalle [5], Alasseur, Taher, and Matoussi [2], Casgrain and Jaimungal [8], Lacker and Soret [26], Féron, Tankov, and Tinsi [14] and [28] who study similar problem in the mean field game framework called mean field game of controls or extended mean field game, as well as our companion paper Djete [9] adapts the arguments of this paper to the context of mean field game of controls.…”

Equilibrium price formation with a major player and its mean field limit

“…A popular phenomenological approach used to fit to the concept of Nash equilibrium is to assume that the relevant asset price is decomposed into two parts; one is a so-called fundamental price, which is exogenously given and assumed to be independent of the agents' actions, and the other part representing the market friction which is often assumed to be proportional to the average trading speed among the agents. One can find in [1,14,16,21,24,32,45] interesting applications to, optimal trading, liquidation, energy production, optimal use of smart grids, etc. In particular, we refer to Fu & Horst [25], Evangelista & Thamsten [19] and Féron et.al.…”