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Probability and Computational Finance Seminar
Leonard Wong
University of Washington
Title: Geometry and Optimization of Relative Arbitrage

Abstract: Consider investing in an equity market. While classical financial theory suggests that the market portfolio is efficient, stochastic portfolio theory shows that the market can be beaten in the long run under realistic assumptions. Moreover, no forecasts of expected returns and covariances are needed to construct such relative arbitrages. Suppose we restrict to portfolios that are deterministic functions of the market weights (firm sizes divided by total market value). Under the conditions of diversity and sufficient volatility, we characterize all portfolios leading to relative arbitrages in two ways: first, as Fernholz's functionally generated portfolios, and second, as solutions to an optimal transport problem. The later leads naturally to an optimization problem, and we will introduce another approach in the spirit of maximum likelihood estimation of a log-concave density. Both approaches will be illustrated with simple empirical examples.

This is joint work with Soumik Pal.

Date: Monday, September 21, 2015
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Kasper Larsen