Scalable Pontryagin-Guided Adjoint-to-Control Recovery for Constrained Dynamic Portfolio Choice

Battle Count: 75

Directly addresses constrained continuous-time multi-asset portfolio choice with consumption, a core problem in quantitative finance. Demonstrates scalability to 100 risky assets with practical constraints (no-short-sale, no-borrowing, consumption caps). The adjoint-to-control recovery framework provides a principled way to improve upon neural policy optimization by enforcing local PMP/KKT optimality conditions. Highly relevant for institutional portfolio management, asset allocation, and dynamic trading strategies under realistic constraints.

Requires expertise in stochastic optimal control theory (PMP, adjoint systems, BSDEs), neural network training (DPO with policy gradients), numerical optimization (QP solvers, Newton-CG barrier methods), and Monte Carlo methods (nested antithetic sampling, conditional projections). The two-stage pipeline involves: (1) training a pointwise-feasible neural actor, (2) freezing and detaching latent outputs, (3) performing fixed-latent OL-BPTT for adjoint harvesting, (4) estimating shifted wealth-row via anchored nested regression, and (5) solving local QP or barrier problems. The mathematical machinery (corner charts, second-order adjoints, generalized Hamiltonians) adds significant theoretical complexity.

Source code, configuration files, and validation scripts are publicly available in a fixed GitHub release. All numerical data are generated synthetically from described models and parameter specifications. Detailed calibration tables, seeds, and evaluation budgets are provided. However, the full mathematical proofs are in a separately submitted Published Appendix, and some supplementary diagnostics reference Online Supporting Information not fully included in the extract.