Online portfolio selection with state-dependent price estimators and transaction costs

Artificial intelligence (A.I.) techniques have been applied to the online portfolio selection (OLPS) problem, a topic attracting increasing attention. In brief, OLPS is the task of sequentially updating the investment portfolio with the continuous update of assets’ prices. In this paper, we study the OLPS problem with transaction costs. First, we study the exact computation of the transaction cost and derive related constant upper and lower bounds, which allow us to take the transaction costs into account when deriving an optimal portfolio in each investment period. Second, considering that assets’ market states switch from time to time and their prices exhibit different behaviors in different market states, we propose the state-dependent exponential moving average method (SEMA), which can accurately predict assets’ returns based on historical return data and assets’ market states. Third, we construct the net profit maximization model (NPM) and the net profit maximization model with a risk parity constraint (NPMRP). Finally, we combine these three parts to build the state-dependent online portfolio selection algorithm (SOPS) for solving the OLPS problem with transaction cost. Our empirical results reveal that the proposed SOPS algorithm can outperform many state-of-the-art OLPS algorithms.