Optimal multi-period leverage-constrained portfolios: A neural network approach
Bibliographic record
Abstract
We present a neural network approach for multi-period portfolio optimization that relaxes the long-only restriction and instead imposes a bound constraint on leverage. We formulate the optimization problem for such a relaxed-constraint portfolio as a multi-period stochastic optimal control problem. We propose a novel relaxed-constraint neural network (RCNN) model to approximate the optimal control. Using our proposed RCNN model transforms the original leverage-constrained optimization problem into an unconstrained one, which makes solving it computationally more feasible. We prove mathematically that the proposed RCNN control model can approximate the optimal relaxed-constraint strategy with arbitrary precision. We further propose to compute the optimal outperforming strategy over a benchmark based on cumulative quadratic shortfall (CS). Using U.S. historical market data from Jan 1926 to Jan 2023, we computationally compare and assess the proposed neural network approach to the optimal leverage-constrained strategy and long-only strategy respectively. We demonstrate that the leverage-constrained optimal strategy can achieve enhanced performance over the long-only strategy in outperforming a benchmark portfolio.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.003 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".