Optimal Decumulation for Retirees using Tontines: a Dynamic Neural Network Based Approach
Bibliographic record
Abstract
We introduce a new approach for optimizing neural networks (NN) using data to solve a stochastic control problem with stochastic constraints. We utilize customized activation functions for the output layers of the NN, enabling training through standard unconstrained optimization techniques. The resulting optimal solution provides a strategy for allocating and withdrawing assets over multiple periods for an individual with a defined contribution (DC) pension plan. The objective function of the control problem focuses on minimizing left-tail risk by considering expected withdrawals (EW) and expected shortfall (ES). Stochastic bound constraints ensure a minimum yearly withdrawal. By comparing our data-driven approach with the numerical results obtained from a computational framework based on the Hamilton-Jacobi-Bellman (HJB) Partial Differential Equation (PDE), we demonstrate that our method is capable of learning a solution that is close to optimal. We show that the proposed framework is capable of incorporating additional stochastic processes, particularly in cases related to the use of tontines. We illustrate the benefits of using tontines for the decumulation problem and quantify the decrease in risk they bring. We also extend the framework to use more assets and provide test results to show the robustness of the control.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".