Reinforcement learning is one of the most fascinating sub-fields of machine learning, which has found a variety of empirical application and actively interact with different disciplines. Particularly in finance, there are many tasks in trading or investment decisions seem well suited for RL approaches. As a typical type of model-free RL, Q-learning algorithm can solve a risk-adjusted Markov decision process for a discrete-time Black-Scholes-Merton model. It proposes a purely data-driven option price which is to be compared with BSM’s result and give suggestions to the traders. A coupling spline algorithm can improve this Q-learning method since there is a key procedure to solve a specific Bellman optimality equation with respect to the Q functions, where it helps to approximate...[ Read more ]

Reinforcement learning is one of the most fascinating sub-fields of machine learning, which has found a variety of empirical application and actively interact with different disciplines. Particularly in finance, there are many tasks in trading or investment decisions seem well suited for RL approaches. As a typical type of model-free RL, Q-learning algorithm can solve a risk-adjusted Markov decision process for a discrete-time Black-Scholes-Merton model. It proposes a purely data-driven option price which is to be compared with BSM’s result and give suggestions to the traders. A coupling spline algorithm can improve this Q-learning method since there is a key procedure to solve a specific Bellman optimality equation with respect to the Q functions, where it helps to approximate the fixed point more efficiently. Currently, the theoretical literature incorperating reinforcement learning methods into finance topics is sparse, and moreover scattered among different financial application areas. Thus there exists huge potential to be explored and exploited in this field.

Keywords:Markov decision process, stochastic approximation, reinforcement learning, Q-learning, coupling spline algorithm, Black-Scholes model, option pricing.