Monetizing Volatility in Portfolio Optimization: Quantifying the Optimality Gap Using Deep FBSDE Approach

Multi-Period Portfolio Optimization (MPO) and Model Predictive Control (MPC) are key advanced tools in the arsenal of quantitative finance professionals, helping to integrate efficient trade scheduling and multi-horizon alpha and risk views. Our research shows that the process of using MPO leaves a substantial amount of money on the table. This sub-optimality is the result of applying deterministic optimal control instead of using stochastic optimal control (SOC), which provides consistent additional premium capture. While exact SOC solution generally is unattainable under realistic transaction costs and constraints, the deep-learning-driven forward-backward stochastic differential equation (FBSDE) solver we propose in this article allows for a “good-enough” approximation of the SOC solution and shows a significant advantage over the MPO.