Dr. Ting-Kam Leonard Wong (University of Washington)

Title: Geometry, Hierarchy and Optimization of Relative Arbitrages

Abstract:A major aim of Stochastic Portfolio Theory is to construct portfolios that outperform the market under minimal and realistic assumptions on market behavior. These portfolios are called relative arbitrages. Two fundamental conditions leading torelative arbitrages are diversity and the presence of sufficient volatility. Under these assumptions functionally generated portfolio is a systematic tool for constructing relative arbitrages. In this talk we will report some recent results concerning these portfolios. First, we characterize these portfolio in terms of a cyclical monotonicity property and optimal transport. Second, we study an ordering among functionally generated portfolios and identify the maximal elements. Finally, we introduce a shape-constrained optimization problem for these portfolios in the spirit of maximum likelihood estimation of a log-concave density. This is joint work with Soumik Pal.