ESSAYS ON ADVANCED METHODS IN PORTFOLIO OPTIMIZATION

Abstract

This dissertation consists of four chapters on my work in developing new methods for financial portfolio optimization. The first chapter introduces the MCTS algorithm to the financial world and focuses on solving significant multi-period financial planning models by combining a Monte Carlo Tree Search algorithm with a deep neural network. The MCTS provides an advanced start for the neural network so that the combined method outperforms either approach alone, yielding competitive results. We compare the two-step algorithm with employing dynamic programs/neural networks. Both approaches solve regime switching models with 50-time steps and transaction costs with twelve assets. Heretofore, these problems have been outside the range of solvable optimization models via traditional algorithms. In the second chapter, we build an end-to-end neural network model to build a portfolio of factors that aims to maximize the Sharpe ratio and show that it significantly outperforms the factor momentum strategy. The performance of the factor portfolio is further improved via a scaling method that relies on a variant of volatility scaling called hybrid scaling. Next, we explore the potential of using the factor portfolio as an overlay to an already existing portfolio of large asset classes. Finally, the effect of transaction costs on the methods is analyzed. In the third chapter, we propose the continuous jump model and the sparse continuous jump model, which are extensions of the jump model and the sparse jump model respectively, for fitting regimes to financial time series. Through various 2-state and 3-state synthetic data simulations, we show that our models yield better, and more robust results compared to their counterparts in terms of model various performance metrics. Finally, we show how our model can be used to fit a regime model to the NASDAQ index. In the final chapter, we introduce pseudo-implicit layers, a fast and practical neural network layer that can be used for portfolio models with various hyper-parameters, including non-differentiable ones. We empirically show through different examples that the pseudo-implicit layers give competitive results.