November-December 2024 : Professor Andrew Philpott is hosted at the CERMICS Laboratory Ecole Nationale des Ponts et Chaussées de Paris . He is a Professor at the University of Auckland New Zealand of Operations Research and co-director of the Electric Power Optimization Center at the University of Auckland. His research interests are in stochastic optimization and game theory and their application to electricity markets.
Title: Geometry of Arrow-Debreu security trades
Abstract: We are motivated by developing a framework for smart-contract design that would help the development and adoption of smart-grid technologies. These contracts would help to hedge risks and make the development of renewable energies, local and smart-consumption more acceptable to users. It is well known that perfectly competitive partial equilibrium corresponds to a social optimum when all agents are risk neutral and share common knowledge of the probability distribution governing uncertainties.
The situation is complicated when agents are risk averse, in which case we need securities available to trade in order to hedge risk. Indeed, assuming that there are enough Arrow-Debreu securities, competitive equilibrium will yield a social optimum (with a suitably defined social risk measure) when agents have nested coherent risk measures with intersecting polyhedral risk sets.
In this project, we aim to study the (polyhedral) geometry of admissible trades, which might depend on each agent’s risk set, and not only their intersection. This study will shed light on what a smart-contract should encompass so that a local market equilibrium would be socially optimal.