Interpretable Optimal Stopping

Optimal stopping is the problem of deciding when to stop a stochastic system obtain greatest reward, arising in numerous application areas such as finance, healthcare, and marketing. State-of-the-art methods for high-dimensional optimal involve approximating value function or continuation then using that approximation within greedy policy. Although policies can perform very well, they are generally not guaranteed be interpretable; is, decision maker may able easily see link between current state policy’s action. In this paper, we propose new approach wherein policy represented binary tree, spirit naturally interpretable tree models commonly used machine learning. We show class rich enough approximate formulate learning from observed trajectories sample average (SAA) problem. prove SAA converges under mild conditions size increases but that, computationally, even immediate simplifications theoretically intractable. thus tractable heuristic approximately solving by greedily constructing top down. demonstrate our applying it canonical option pricing, both synthetic instances real Standard & Poor’s 500 Index data. Our method obtains (1) outperform state-of-the-art noninterpretable methods, based on simulation regression martingale duality, (2) possess remarkably simple intuitive structure. This paper was accepted Chung Piaw Teo, Management Science Special Section Data-Driven Prescriptive Analytics.