Titles and Abstracts
Smoothness of directed chain stochastic differential equations and its applications
Tomoyuki Ichiba (University of California at Santa Barbara)
Abstract: On a filtered probability space for the space of continuous functions, we shall consider a system of stochastic equations called directed chain stochastic differential equations for a pair of stochastic processes whose marginal distributions in the path space are identical and their joint distribution is uniquely determined by the system of equations with the distributional constraints. In this talk we discuss the smoothness of the solutions of the equations under some regular conditions first, and then consider some relaxation of the conditions on the coefficients and the distributional constraints. We also introduce its financial applications of such systems in the generative adversarial network problem.
Bio: Tomoyuki Ichiba is currently a professor and department chair in the Department of Statistics and Applied Probability at University of California Santa Barbara. He received PhD in Statistics from Columbia University in 2009. His recent research interests include Stochastic Analysis and its applications to mathematical finance, machine learning and quantum computing.
Mean field games with partial information
Thaleia Zariphopoulou (University of Texas at Austin)
Abstract: I will present mean field games in portfolio choice under relative performance concerns, and under partial information for the stock's drift. I will derive a master system (the master equation and a compatibility condition for the optimal mean field controls) and construct solutions for a large class of utilities (beyond homothetic) and general couplings. The solutions combine elements of the single agent problem (no competition) with partial information and of indifference valuation of a claim written on the optimal aggregate wealth. I will, also, present new results on the solution of the former problem, together with representative examples. If time permits, I will discuss the model and related questions when formulated in the extended setting of forward utilities.
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 statutory Oxford-Man Chair in Quantitative Finance at the Mathematical Institute, University of Oxford. She is an associate faculty member of the Oxford-Man Institute of Quantitative Finance and has held visiting positions at the Mathematical Institute, University of Oxford.
Her area of expertise is Financial Mathematics and Stochastic Optimization. She has published extensively in the areas of investments and valuation in incomplete markets, and introduced novel approaches to indifference valuation, risk measures and stochastic utilities. She has served very actively the community of Financial Mathematics. She sits on the editorial board of twelve academic journals and monograph series, and she is the Editor of the SIAM Book 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.
