Author : Jorge Guijarro Ordonez
Release : 2021
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Kind : eBook
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Book Synopsis Stochastic Control and Deep Learning Approaches to High-dimensional Statistical Arbitrage by : Jorge Guijarro Ordonez
Download or read book Stochastic Control and Deep Learning Approaches to High-dimensional Statistical Arbitrage written by Jorge Guijarro Ordonez. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt: The central problem of this dissertation is the mathematical study of statistical arbitrage in the case of a high-dimensional number of assets, which is analyzed from two complementary approaches. In the first part of the dissertation, we consider the problem from a stochastic control perspective that extends and combines the Avellaneda and Lee model for statistical arbitrage with the classical Merton framework for portfolio theory. In our framework, given a high-dimensional number of assets and a mean-reverting stochastic model for the dynamics of their residuals through a statistical factor model, an investor must decide how to trade the original assets to maximize the expected utility of her terminal wealth in a finite time horizon, while taking into account market frictions and common statistical arbitrage constraints like dollar neutrality. We study continuous-time and discrete-time versions of the trading problem with both exponential utility and a mean-variance objective, and we prove the existence of interpretable analytic or semi-analytic optimal trading strategies through the study of the corresponding Hamilton-Jacobi-Bellman partial differential equations. We supplement this theoretical study with extensive Monte Carlo simulations that provide further insight about the qualitative behavior of the found optimal strategies under different parameter regimes. In the second part of the dissertation, we complement the previous study with a general deep-learning framework that mitigates two limitations of the stochastic control approach: strong modeling assumptions on the residual dynamics, and solving the high-dimensional Hamilton-Jacobi-Bellman equations for more realistic objective functions, models, and constraints. To this end, we frame the residual modeling and trading problems as a double optimal control problem, that we solve numerically by restricting the controls to a series of functional classes that range from classical parametric models to the most advanced neural network architectures adapted to our problem. We test these methods by conducting an extensive out-of-sample empirical study with high-capitalization U.S. equity data over the main families of factor models, which provides a comprehensive analysis of the importance of the different elements of a statistical arbitrage strategy and the gains from machine learning methods.
