## Overview

The research in Applied Mathematics I have been conducting with my co–authors during the past few years, has been motivated so far by two main words: *interactions* and *incentives*. These two terms have to be related in the context of my work to the Economics field, and in particular when focusing on the behaviour of economic actors. The term interaction thus refer to interaction between consumers, workers, more generally called *Agents*, through their decisions, their actions, the price they pay for a service, or even through an external parameter. When looking at interactions, the aim is generally to find an equilibrium in this game between the Agents, so that no one has an interest in deviating. This so–called Nash equilibrium can be extended in the case of a continuum of Agents, and then reaches a more recent theory borrowed from Physics, the Mean–Field Games. The term incentives also has an economic content, and refer to the Contract Theory, and more precisely to Principal–Agents problems. In this case, an Agent (he) is delegated to act on behalf of a *Principal* (she). The Principal's purpose is to find appropriate incentives, in the form of a contract, to encourage the Agent to act in her interest. When considering these issues from the mathematical point of view, the behaviour of Agents, in an uncertain environment and in continuous–time, can be modelled as a *stochastic control* problem. My research so far is thus a continuous path oscillating between Principal–Agent problems, Nash equilibria and Mean–Field Games, using recently introduced and state of the art tools in stochastic control.

## Publications

- Romuald Elie, Emma Hubert, Thibaut Mastrolia, and Dylan Possamaï. Mean–field moral hazard for optimal energy demand response management.
*Mathematical Finance*, to appear, 2021. - Romuald Elie, Emma Hubert, and Gabriel Turinici. Contact rate epidemic control of COVID-19: an equilibrium view.
*Mathematical Modelling of Natural Phenomena**,*15(35):1–25, 2020. - Emma Hubert and Gabriel Turinici. Nash–MFG equilibrium in a SIR model with time dependent newborn vaccination.
*Ricerche di matematica*, 67(1):227–246, 2018.

## Preprints

4. Clémence Alasseur, Corinne Chaton, and Emma Hubert. Optimal insurance contract with benefits in kind under adverse selection. *Preprint **arXiv:2001.02099*, 2020.

5. Emma Hubert. Continuous–time incentives in hierarchies, *Preprint **arXiv:2007.10758**, *2020.

6. Emma Hubert, Thibaut Mastrolia, Dylan Possamaï and Xavier Warin. Incentives, lockdown, and testing: from Thucydides's analysis to the COVID–19 pandemic. *Preprint **arXiv:2009.00484*, 2020.

## Working papers

7. Thibaut Mastrolia and Emma Hubert. Multidimensional 2BSDEs and link with Nash equilibrium.

8. Romuald Elie, Emma Hubert, and Adrien Nguyen–Huu. A Real Option Mean–Field Game.