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Mathematics Colloquium

David Itkin
Imperial College

Title: Equity Modelling in Stochastic Portfolio Theory and Portfolio Optimization with Frictions; Empirics, Robustness and Transaction Costs
Date: Monday, January 22, 2024
Place and Time: Love 101, 3:05-3:55 pm

Abstract. In mathematical finance, the modelling of equity markets and questions regarding portfolio selection are fundamental to practitioners, regulators and academics alike. This talk gives an overview of recent results in Stochastic Portfolio Theory and transaction costs modelling, with the aim of developing practically implementable models and trading rules. Concretely, building on previously proposed volatility stabilized models (Fernholz & Karatzas, 2005), we propose a rank-based extension to model a high-dimensional equity market over long time horizons. Theoretical properties of the model are established and statistical estimators for the parameters are developed, which are subsequently calibrated to historical equity data. A robust growth-optimization problem is then considered in a general incomplete market setting with performance guarantees and a characterization of the optimal strategy established. Lastly, we look at the performance of linear strategies in a setting where an investor with mean-variance preferences has access to a noisy signal of future asset returns and faces superlinear transaction costs. We show that under realistic choices of the parameters the best strategy in this class performs nearly as well as the true optimum, which we compute with a brute force numerical method. Our result gives a simple and practical rule of thumb that can be efficiently implemented and yields nearly optimal performance.