Analysis of a penalty method for pricing a guaranteed minimum withdrawal benefit (GMWB)
Why this work is in the frame
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Bibliographic record
Abstract
The no arbitrage pricing of Guaranteed Minimum Withdrawal Benefits (GMWB) contracts results in a singular stochastic control problem which can be formulated as a Hamilton Jacobi Bellman (HJB) Variational Inequality (VI). Recently, a penalty method has been suggested for solution of this HJB variational inequality (Dai et al., 2008). This method is very simple to implement. In this article, we present a rigorous proof of convergence of the penalty method to the viscosity solution of the HJB VI. Numerical tests of the penalty method are presented which show the experimental rates of convergence, and a discussion of the choice of the penalty parameter is also included.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it