THREE ESSAYS IN MODERN PORTFOLIO THEORY

Abstract

This work contains three projects about portfolio management. In the first project we use deep learning approach to solve portfolio management problem with proportional transaction cost. Deep neural networks are built up to approximate singular optimal controls and thus the trading strategies. We justify that deep learning framework can be applied to high-dimensional problem where other existing numerical methods cannot. The second project is about the utility maximization problems in stochastic volatility environment. We use backward stochastic differential equation with jump to characterize the optimality condition, and simplify the solution of BSDEJ by an ordinary differential equation. We solve a min-max problem of robust exploratory mean-variance optimization in the third project considering the drift uncertainty. Reinforcement learning framework in mean-variance problem provides an exploration-exploitation trade-off mechanism; if we additionally consider model misspecification, robust strategy essentially weights more on exploitation rather than exploration and thus reflects a more conservative optimization scheme.