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This paper studies speculative trading as a sequential optimal stopping problem, using an exploratory reinforcement learning (RL) framework with entropy regularization. The problem is relaxed by modeling stopping times as jump times of Cox processes driven by bounded intensity controls. The authors derive closed-form solutions for the optimal policy via exploratory HJB equations and Gibbs distributions, and provide error estimates and convergence guarantees.
Closed-form solutions for optimal speculative trading policies are now possible using entropy-regularized reinforcement learning, offering a tractable alternative to complex numerical methods.
We study a speculative trading problem within the exploratory reinforcement learning (RL) framework of Wang et al. [2020]. The problem is formulated as a sequential optimal stopping problem over entry and exit times under general utility function and price process. We first consider a relaxed version of the problem in which the stopping times are modeled by the jump times of Cox processes driven by bounded, non-randomized intensity controls. Under the exploratory formulation, the agent's randomized control is characterized via the probability measure over the jump intensities, and their objective function is regularized by Shannon's differential entropy. This yields a system of the exploratory HJB equations and Gibbs distributions in closed-form as the optimal policy. Error estimates and convergence of the RL objective to the value function of the original problem are established. Finally, an RL algorithm is designed, and its implementation is showcased in a pairs-trading application.