There is a PhD position available at Centrale Supélec Université Paris-Saclay.

Topic description: Electricity retail pricing is increasingly shaped by volatility, renewable uncertainty, and the growing role of flexible assets. This thesis aims to design tariffs and incentive contracts that create value from flexibility while managing risk in realistic market conditions.

Deterministic framework. In the static setting, nonlinear pricing and screening problems have recently seen major breakthroughs, including the works Carlier, Zhang for general existence results under adverse selection, Figalli, Kim, and McCann for convexity results in the quasi-linear case, McCann, Zhang for fully nonlinear models and the two-dimensional Rochet–Choné characterization. This PhD project will extend this line of research by introducing a genuinely dynamic (time-dependent) formulation and developing the corresponding theoretical results (e.g., existence, structural properties, and principled characterizations), while maintaining close contact with energy-market interpretations.

Stochastic extension. Real markets are uncertain: prices spike, forecasts err, and operational constraints matter. In continuous-time settings, the classical Holmström-Milgrom paradigm models output as a diffusion process where the drift is controlled by the agent. This framework was significantly extended by Sannikov, who introduced the agent’s continuation value as a key state variable. More recent literature leverages dynamic programming and (2)BSDE techniques to design contracts that may also depend on quadratic variation. These advanced mathematical tools are uniquely suited to energy applications, where intrinsic uncertainty and stringent risk constraints are paramount.

Candidate profile: Strong background in analysis, probability, optimization, PDE and related areas; interest in energy systems and real-world modelling; prior exposure to economics is not required; coding skills are a plus.

Contact: No specific deadline for applications. The expected starting date is 2027, for a 3-year PhD under the CIFRE industrial format. Please email a CV and a short statement of interest (and optionally transcript + reference contacts) to Gaoyue Guo — gaoyue.guo@centralesupelec.fr