Peter Carr Seminar Series: Rene Aid and Leonard Wong
Registration is required to attend in person.
Rene Aid (Paris-Dauphine University)
Title
Continuous-Time Persuasion by Filtering
Abstract
We frame dynamic persuasion in a partial observation stochastic control Leader-Follower game with an ergodic criterion. The Receiver controls the dynamics of a multidimensional unobserved state process. Information is provided to the Receiver through a device designed by the Sender that generates the observation process. The commitment of the Sender is enforced. We develop this approach in the case where all dynamics are linear and the preferences of the Receiver are linear-quadratic. We prove a verification theorem for the existence and uniqueness of the solution of the HJB equation satisfied by the Receiver’s value function. An extension to the case of persuasion of a mean field of interacting Receivers is also provided. We illustrate this approach in two applications: the provision of information to electricity consumers with a smart meter designed by an electricity producer; the information provided by carbon footprint accounting rules to companies engaged in a best-in-class emissions reduction effort. In the first application, we link the benefits of information provision to the mispricing of electricity production. In the latter, we show that even in the absence of information cost, it might be optimal for the regulator to blur information available to firms to prevent them from coordinating on a higher level of carbon footprint to reduce their cost of reaching a below-average emission target. Joint work with Ofelia Bonesini, Giorgia Callegaro, and Luciano Campi.
Bio
Professor of economics at Paris-Dauphine University since 2016 and lecturer at the Ecole Polytechnique (2015-2018), Africa Business School Affiliate since 2019. EDF R&D research engineer in financial economics of energy markets (1998-2003) and manager (2003-2006). Co-founder and Director (2006-2013) of the Finance for Energy Markets Research Initiative. Deputy Director of EDF R&D Research Department on generation and financial risk management (2014-2016). Author of the monography Electricity Derivatives, Springer, 2015. Holder of a patent on demand response management. Director of the Dauphine Master Program Economics & Finance (2017-2022). Principal investigator of the ANR project MIRTE from the PEPR Math-VIVES.
Leonard Wong (University of Toronto)
Title
A mathematical study of the excess growth rate
Abstract
The excess growth rate, also called the diversification return, is a fundamental concept in portfolio theory: it captures the profit of a portfolio due to rebalancing and quantifies the intrinsic volatility of a stock market. In this talk, we undertake an in-depth mathematical study of this object and explore its connections to familiar concepts in information theory like the relative, Rényi and cross entropies, the Helmholtz free energy, L. Campbell's measure of average code length, and large deviations. Our main results consist of three characterization theorems for the excess growth rate in terms of (i) the relative entropy, (ii) the gap in Jensen's inequality, and (iii) the logarithmic divergence that generalizes the Bregman divergence. We also discuss the maximization of the excess growth rate and compare it with the growth optimal portfolio. Based on joint work with Steven Campbell.
Bio
Ting-Kam Leonard Wong received the B.Sc. and M.Phil. degrees from The Chinese University of Hong Kong and the Ph.D. degree in Mathematics from the University of Washington. He is currently an Associate Professor at the Department of Statistical Sciences, University of Toronto. Before joining the University of Toronto in 2018, he spent two years at the University of Southern California as a non-tenure track Assistant Professor in financial mathematics. His current research interests include mathematical finance, probability, optimal transport, information geometry, as well as applications in statistics and machine learning. He is an associate editor of the journal Information Geometry.