Paper on deep learning operator splitting method for American option pricing released

Dong Yan, Haocheng Zhu, and Yao Li published an academic paper proposing a deep learning-driven operator splitting scheme for high-dimensional free boundary problems, applied to American option pricing under incomplete markets. The pricing problem corresponds to a market with proportional transaction costs, stochastic liquidity risk with nonlinear drift validated on S&P 500 data, and two-factor stochastic volatility, formulated as a five-dimensional highly nonlinear variational inequality. The scheme decomposes it by time layer into an elliptic continuation equation approximated by physics-informed neural networks, and a closed-form projection step enforcing early exercise constraints, deriving conditional ℓ∞ stability bounds under given pre-solution and Lipschitz assumptions. The scheme is validated against finite difference and least-squares Monte Carlo benchmarks, with option prices and learned exercise boundaries closely matching reference solutions.

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