This paper is the first attempt at a general non-Markovian theory of time-inconsistent stochastic control problems in continuous-time. We consider sophisticated agents who are aware of their time-inconsistency and take into account in future decisions. We prove here that equilibria in such a problem can be characterised through a new type of multi-dimensional system of backward SDEs, for which we obtain wellposedness. Unlike the existing literature, we can treat the case of non-Markovian dynamics, and our results go beyond verification type theorems, in the sense that we prove that any (strict) equilibrium must necessarily arise from our system of BSDEs. This is a joint work with Camilo Hernández, Columbia University.
Bio: Dylan Possamaï’s research interests span several areas of applied mathematics, including optimization and stochastic control, backward stochastic differential equations, and stochastic analysis, in mathematical finance and economics. Applications areas for his work include robust finance, contract theory, electricity markets, and general incentives problems in economics. Prior to joining Columbia Engineering in 2017, Possamaï was a tenured assistant professor at Université Paris Dauphine in France from 2012 to 2016. He earned his PhD in 2011 from École Polytechnique, France; his MS in 2009, from UPMC Sorbonne Universités, and his BS in 2009 from École Polytechnique. He received the best young research in finance and insurance award of the Europlace Institute of Finance in 2017.