Random concave functions

Thursday, December 21, 2017 - 16:00 to 16:50
427 Thackeray
Speaker Information
Professor Leonard Wong
Department of Mathematics, University of Southern California

Abstract or Additional Information


Concave and convex functions arise naturally in various applications. In this talk we are 
interested in constructing random realizations of these objects, i.e., probability measures 
on spaces of concave functions. First we motivate this problem with nonparametric 
Bayesian statistics and T. Cover's universal portfolio in connection with stochastic 
portfolio theory. In the second part of the talk we study a model of generating random concave
 functions on the simplex by taking the minimum of independent random hyperplanes. We present 
interesting results about the limiting distribution as the number of hyperplanes tends to infinity, 
and show that it can be described via duality by Poisson point processes.
This is on-going work with Peter Baxendale (USC), Christa Cuchiero (Vienna) and Walter Schachermayer (Vienna).