Mykhaylo Shkolnikov — Princeton University

Title: Gaussian fluctuations in rank-based models of stochastic portfolio theory

Abstract: The rank-based models introduced by Robert Fernholz assume that the dynamics of market capitalizations of companies only depend on their rank. It is known that within such models the capital distribution curve approaches a limiting shape described by the porous medium equation when the number of companies is large. In this talk I will show that the fluctuations of the capital distribution curve around its limit shape are given by a Gaussian process and explain how one can understand the covariance structure of that process. This is joint work with Praveen Kolli.