INEUS: Iterative Neural Solver for High-Dimensional PIDEs

Battle Count: 65

Highly relevant to quantitative trading and financial engineering. The paper directly addresses high-dimensional option pricing under jump-diffusion models (Black-Scholes PIDEs with default risk), which are core problems in derivatives pricing and risk management. The ability to handle 100+ dimensional problems with jumps makes it applicable to basket options, portfolio risk, and multi-asset derivatives. The nonlinear Black-Scholes PIDE with default risk is directly relevant to credit risk modeling. However, the method is a general PIDE solver rather than a trading-specific tool, and practical deployment would require integration with market data pipelines and real-time computation infrastructure.

High implementation complexity due to: (1) DGM architecture with multiple gated layers and hPINN encoding for boundary conditions, (2) iterative training with inner recursion steps and frozen target networks, (3) Polyak averaging with periodic regression/distillation onto the hPINN class, (4) directional differentiation trick to avoid full Hessian computation, (5) residual-adaptive sampling (RAD) combined with path-based sampling, (6) careful hyperparameter tuning of alpha, h, n, xi, and K, (7) handling of boundary conditions via distance functions, (8) single-jump sampling with variance management. The algorithm requires understanding of both neural network training and PIDE theory.

The paper provides a detailed algorithm (Algorithm 1), full network architecture (DGM with hPINN encoding), specific hyperparameters (batch size M=1024, inner steps n=20, gradient steps N=32, learning rate 0.0005, alpha=0.4, h=0.5, K=10), and benchmark problems with closed-form or Monte Carlo reference solutions. However, no GitHub repository or code link is provided. The implementation uses TensorFlow/Keras with GPU acceleration on NVIDIA RTX 4090. All test parameters and sampling strategies (RAD, path-based) are specified.