Consumers satisfy their electricity demand by self-production (solar panels) and centralized production (energy companies). Both companies and consumers are interested in characterizing the production strategies which minimize the costs and satisfy some properties; in particular, consumers need low-variance policies so as to have a stable flux of energy, whereas companies face carbon taxes and a penalty in case of under/overproduction. We address three problems: namely, we consider the point of view of a representative consumer, a representative energy company and a social planner. We deal with McKean-Vlasov control problems with stochastic coefficients and provide explicit formulas for the optimal strategies of each problem; finally, we compare the results and look for an electricity price such that the optimal controls asymptotically coincide in mean. Based on a joint work with R. Aïd, I. Ben Tahar and H. Pham.

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