A Monotone Limit Approach to Entropy-Regularized American Options

Battle Count: 95

Directly relevant to American option pricing, a core problem in quantitative trading. The entropy-regularized framework connects optimal stopping with reinforcement learning, enabling policy-based interpretations useful for algorithmic trading. The PIA provides a practical computational method for pricing American-style derivatives. However, the paper is primarily theoretical with limited numerical validation, and the connection to actual trading strategies (execution, hedging) is indirect.

Implementation requires: (1) solving BSDEs numerically via Monte Carlo with least-squares regression, (2) iterative PIA with linear BSDE solves at each step, (3) careful handling of the exponential policy form for numerical stability, (4) lambda scheduling for convergence speed. The mathematical framework is sophisticated (RBSDEs, Doob-Meyer decomposition), and practical implementation demands expertise in stochastic analysis and numerical methods. The 2000-iteration PIA with 100,000 paths is computationally intensive.

The paper provides detailed mathematical derivations, algorithm descriptions, and a numerical experiment with specified parameters (d=2, K=100, r=0.05, sigma=0.2, delta=0.1, T=3, N=100, 100000 paths, 2000 PIA iterations). However, no code repository is provided. The methodology relies on standard BSDE theory and least-squares regression (Andersen-Broadie basis functions), making reproduction feasible for experts but requiring significant implementation effort.