Continuous-time reinforcement learning approach for portfolio management with time penalization

This paper considers the problem of policy optimization in the context of continuous-time Reinforcement Learning (RL), a branch of artificial intelligence, for financial portfolio management purposes. The underlying asset portfolio process is assumed to possess a continuous-time discrete-state Markov chain structure involving the simplex and ergodicity constraints. The goal of the portfolio problem is the redistribution of a fund into different financial assets. One general assumption has to be set, namely that the market is arbitrage-free (no price arbitrage is possible) then the problem of how to obtain the optimal policy is solvable. We provide a RL solution based on an actor/critic architecture in which the market is characterized by a restriction called transaction cost, involving time penalization. The portfolio problem in Markov chains is determined by solving a convex quadratic minimization problem with linear constraints. Any Markov chain is generated by a stochastic transition matrices and the mathematical expectations of the rewards. In particular, we estimate the elements of the transition rate matrices and the mathematical expectations of the rewards. This method learns the optimal strategy in order to make a decision on what portfolio weight to take for a single period. With this strategy, the agent is able to choose the state with maximum utility and select its respective action. The optimal policy computation is solved employing a proximal optimization novel approach, which involves time penalization in the transaction costs and the rewards. We employ the Lagrange multipliers approach to include the restrictions of the market and those that are imposed by the continuous time frame. Moreover, a specific numerical example in baking, that fit into the general framework of portfolio, validates the effectiveness and usefulness of the proposed method.