A General Framework of Optimal Investment

Abstract

In this paper, we propose a general framework of optimal investment and a collection of trading ideas, which combine probability and statistical theory with, potentially, machine learning techniques, e.g., machine learning regression, classification and reinforcement learning. The trading ideas are easy to implement and their validity is justified by full mathematical rigor. The framework is model-free and can, in principle, incorporate all categories of trading ideas into it. Simulation and backtesting studies show good performance of selected trading strategies under the proposed framework. Sharpe ratios are above 8.00 in simulation study and Sortino ratios are above 4.00 in backtesting, with very limited drawdowns, using 20 years of monthly data of US equities (NASDAQ, NYSE and AMEX from 1999.1 to 2018.12) and 17 years of monthly data of China A-Share equities (Shanghai and Shenzhen Stock Exchange from 2002.1 to 2018.8).