Reinforcement Learning in Real Option Models

TL;DR

This paper introduces an entropy-regularized reinforcement learning framework for optimal stopping problems inspired by real options, enabling randomized policies and providing algorithms with convergence guarantees.

Contribution

It develops a novel entropy-regularized approach to optimal stopping, deriving explicit solutions, proving convergence, and proposing model-based and model-free algorithms for data-driven decision making.

Findings

Explicit analytical solution to the regularized problem.

Convergence of the free boundary to classical thresholds as entropy vanishes.

Strong numerical performance of proposed algorithms.

Abstract

We investigate an entropy-regularized reinforcement learning (RL) approach to optimal stopping problems motivated by real option models. Classical stopping rules are strict and non-randomized, limiting natural exploration in RL settings. To address this, we introduce entropy regularization, allowing randomized stopping policies that balance exploitation and exploration. We derive an explicit analytical solution to the regularized problem and prove convergence of the associated free boundary to the classical stopping threshold as the entropy vanishes. The regularized problem admits a natural formulation as a singular stochastic control problem. Building on this structure, we propose both model-based and model-free policy iteration algorithms to learn the optimal boundary. The model-free method operates without knowledge of system dynamics, using only trajectories from the stochastic environment. We establish convergence guarantees and illustrate strong numerical performance. This framework provides a principled and tractable approach for data-driven stopping problems under uncertainty.