Speaker: Ting-Kam Leonard Wong
Title: Excess growth rate in finance and beyond
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 relative volatility of a stock market. In this talk I present our study of the excess growth rate in relation to optimal transport and information theory/geometry. We show that as a cost function in optimal transport, it leads to a multiplicative analogue of Brenier’s theorem. As a logarithmic divergence (that extends the Bregman divergence), it can be linked to the Dirichlet perturbation, Rényi divergence and large deviation, and satisfies a generalized Riemannian Pythagorean theorem. We also present axiomatic characterizations of the excess growth rate in terms of its financial properties and connections with the relative entropy and the logarithmic divergence. Based on joint works with S. Pal, J. Zhang, and S. Campbell.