Deep Learning for Reflected BSDEs: Regularization and Error Analysis

Battle Count: 98

Highly relevant for quantitative trading and derivatives pricing. The paper directly addresses American option pricing in high dimensions, which is a core challenge in quantitative finance. The reflected BSDE formulation allows direct treatment of continuous-time early exercise (rather than Bermudan approximation), which is more accurate for pricing American-style derivatives. The methods can be applied to basket options, max options, and geometric options commonly traded in financial markets. The high-dimensional capability (tested up to 200 dimensions) makes it practical for portfolio-level derivative pricing and hedging.

Moderate to high complexity. Requires understanding of BSDE theory, stochastic calculus, and the regularization framework. The neural network architecture is relatively simple (3 hidden layers, ReLU), but the training procedure involves careful handling of the backward recursion, batch normalization, and learning rate scheduling. The obstacle decomposition (identifying U, V, A processes) requires domain-specific knowledge for each payoff type. The error analysis is mathematically sophisticated but not needed for implementation. PyTorch-based implementation with standard optimization (Adam) reduces some complexity.

The paper provides detailed algorithm descriptions (DFS and DBS), specific hyperparameters (network architecture: 3 hidden layers with d+10 neurons, ReLU activation, batch normalization, Adam optimizer with learning rate 5e-3, batch size 512, 3000 iterations for DBS, 5000 for DFS), hardware specifications (AMD Ryzen 9 9950X, 96GB RAM, NVIDIA RTX 5090), and implementation details (PyTorch). However, no code repository is explicitly linked. The regularization parameter choice (ε=h) and benchmark methods (binomial tree, Monte Carlo) are clearly specified.