Scalable Pontryagin-Guided Adjoint-to-Control Recovery for Constrained Dynamic Portfolio Choice
Abstract
We study continuous-time multi-asset portfolio choice and consumption under smooth pointwise constraints, including state-dependent feasible sets. The method separates dynamic information acquisition from local constrained recovery. A pointwise-feasible neural actor generates reference rollouts; after training, its realized latent outputs are frozen and first- and second-order adjoints are harvested from a fixed-latent open-loop backpropagation-through-time graph. Feedback therefore generates the reference trajectory without restricting the adjoint formulation to Markov controls. Conditional on the harvested adjoints, deployment solves a local generalized Pontryagin-Hamiltonian problem: quadratic-affine portfolio blocks are recovered exactly by a quadratic program, while a log barrier approximates more general regular KKT branches. We establish local chart representations, an OL-BPTT-to-adjoint correspondence retaining orthogonal martingale residuals, and an end-to-end bound from reference value loss and numerical errors to recovered-policy and local QP-gap errors. Analytical constant- and predictable-opportunity benchmarks validate the adjoints. Common-input experiments show that recovery reduces residual PMP/KKT error left by finite-budget direct policy optimization, including under a state-dependent consumption cap and with up to 100 risky assets. Scalability concerns the constrained action block rather than dimension-free state-space complexity.
Related
- Self-Consistent Adjoint Policy Iteration for Constrained Dynamic Portfolio Choice
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BibTeX
@misc{jeon2026scalable,
title = {{Scalable Pontryagin-Guided Adjoint-to-Control Recovery for Constrained Dynamic Portfolio Choice}},
author = {Jaegi Jeon and Jeonggyu Huh and Hyeng Keun Koo and Byung Hwa Lim},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.15667},
eprint = {2608.15667},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.15667},
}
RIS
TY - UNPB
TI - Scalable Pontryagin-Guided Adjoint-to-Control Recovery for Constrained Dynamic Portfolio Choice
AU - Jaegi Jeon
AU - Jeonggyu Huh
AU - Hyeng Keun Koo
AU - Byung Hwa Lim
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.15667
UR - https://arxiv.org/abs/2608.15667
AB - We study continuous-time multi-asset portfolio choice and consumption under smooth pointwise constraints, including state-dependent feasible sets. The method separates dynamic information acquisition from local constrained recovery. A pointwise-feasible neural actor generates reference rollouts; after training, its realized latent outputs are frozen and first- and second-order adjoints are harvested from a fixed-latent open-loop backpropagation-through-time graph. Feedback therefore generates the reference trajectory without restricting the adjoint formulation to Markov controls. Conditional on the harvested adjoints, deployment solves a local generalized Pontryagin-Hamiltonian problem: quadratic-affine portfolio blocks are recovered exactly by a quadratic program, while a log barrier approximates more general regular KKT branches. We establish local chart representations, an OL-BPTT-to-adjoint correspondence retaining orthogonal martingale residuals, and an end-to-end bound from reference value loss and numerical errors to recovered-policy and local QP-gap errors. Analytical constant- and predictable-opportunity benchmarks validate the adjoints. Common-input experiments show that recovery reduces residual PMP/KKT error left by finite-budget direct policy optimization, including under a state-dependent consumption cap and with up to 100 risky assets. Scalability concerns the constrained action block rather than dimension-free state-space complexity.
ER -