Past Event: Babuška Forum

Mean-Field and N-agent games for optimal investment under relative performance criteria

Thaleia Zariphopoulou, Mathematics and IROM, Presidential Chair in Mathematics and V.F. Neuhaus Professor of Finance, UT Austin

Abstract

In this talk, I will introduce a family of stochastic optimization problems under relative performance criteria, for agents having CARA or CRRA utilities and acting in a common time horizon in log-normal environments. I will present the explicit time-independent equilibrium strategies for both the finite population games and the corresponding mean field games, which are shown to be unique in the class of time-independent equilibria. I will also discuss extensions related to filtering and incomplete information, random horizons, and real-time learning of market dynamics. Bio Thaleia Zariphopoulou is the holder of the Presidential Chair of Mathematics and the V.F. Neuhaus Professorship of Finance at the University of Texas at Austin. Previously, she was the Laun Professor at the University of Wisconsin, Madison and from 2009-2012, the first holder of the Oxford-Man Chair in Quantitative Finance at the University of Oxford. Currently, she is also a Visiting Professor at the Mathematical Institute at Oxford University and a Visiting Member of the FDT Center for Intelligent Asset Management, Columbia University. Her area of expertise is financial mathematics, quantitative finance and stochastic optimization. She has published extensively in the areas of investments and valuation in incomplete markets, and introduced novel approaches to indifference valuation and dynamic risk preferences. She has served very actively the community of financial mathematics and quantitative finance. She sits on the editorial board of eleven academic journals and monograph series, and she is the Editor of the SIAM Series in Financial Mathematics. She has served in various prize committees and panels. She has also been the Vice-Chair (2007-2010) of the SIAG Activity Group in Financial Mathematics and Engineering, and has served as Vice-President (2004-2006) and President (2006-2008) of the Bachelier Finance Society. In 2012, she was elected SIAM Fellow and in 2014, she was an invited speaker at the International Congress of Mathematicians in Seoul.