A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent Lévy Jumps

Battle Count: 68

Directly addresses portfolio optimization under Lévy jump dynamics, which is central to quantitative trading in equity markets with crash risk. The diagnostic protocol is critical for validating neural solvers used in production portfolio optimization. The CRRA-Merton-VG framework, VaR/CVaR analysis, and multi-asset portfolio results are directly applicable to institutional portfolio management. However, the paper is primarily methodological (a verification protocol) rather than proposing a new trading strategy, and the benchmark used is homogeneity-collapsing (not requiring neural solvers). The practical impact is in ensuring correctness of jump-aware portfolio optimizers rather than generating alpha.

High complexity: requires implementing residual-trained neural PDE solvers with automatic differentiation, importance-weighted Monte Carlo integration of Lévy integrals, multiple finite-difference reference solvers with disjoint discretizations, semi-analytic homogeneity-reduction baselines, per-component Hamiltonian decomposition, and surface-level derivative comparisons. The neural architecture uses residual blocks with sinusoidal time encoding, GELU activations, and joint value-policy optimization. The diagnostic protocol itself is conceptually simple but requires careful implementation of multiple independent solvers and systematic comparison infrastructure.

Full code release at GitHub with all solver sources, experiment driver scripts, result JSONs backing every numeric claim, frozen seed lists {42,123,999,7,2024}, hardware/software protocol (Python 3.11, PyTorch 2.9.1, Apple M1 CPU), consistency log for term-by-term verification, and MD5-archived supplement. S&P 500 calibration scripts and fitted parameters provided; raw data not redistributed for legal reasons but schema and reproduction instructions included.