mathfin-data-analysis
GitHub用于数学金融理论论文中数值实验的设计与审计，确保计算支持定理证明而非实证分析。指导如何严谨、可复现地展示收敛性与误差，使数值结果从属于理论贡献。
触发场景
安装
npx skills add brycewang-stanford/Awesome-Journal-Skills --skill mathfin-data-analysis -g -y
SKILL.md
Frontmatter
{
"name": "mathfin-data-analysis",
"description": "Use when designing or auditing the numerical-experiments part of a Mathematical Finance (Wiley) manuscript — at this theory-first venue that means illustrative computation that SUPPORTS a proof (convergence, error bounds, qualitative behavior), never empirical data analysis. Keeps numerics rigorous, reproducible, and subordinate to the theorems."
}
Numerical Experiments (mathfin-data-analysis)
Note on framing
This is a theory-first journal. Mathematical Finance explicitly states that numerical experiments are welcome only when accompanied by a rigorous analysis supporting the theoretical developments, and that routine application of computational methods to financial data will not be considered. So "data analysis" here is not empirical estimation — it is numerical work that illustrates or stress-tests a theorem. This skill is deliberately lighter than its empirical-journal counterpart.
When to trigger
- You want to add simulations or a numerical scheme to a proof-based paper
- A referee may ask whether your theorem "does anything" beyond existence
- You need to show convergence, accuracy, or qualitative behavior predicted by the theory
How to keep numerics journal-appropriate
- Tie every experiment to a result. Each figure/table should illustrate a specific theorem, proposition, or rate (e.g., "Monte Carlo error decays at the proven $O(n^{-1/2})$ rate", "the free boundary matches the smooth-fit characterization").
- State the method precisely. Discretization scheme (Euler–Maruyama, Milstein, PDE finite-difference/finite-element), step sizes, number of paths, variance reduction, truncation of the domain — enough that the experiment is reproducible.
- Report error, not just output. Where the theory gives a rate or bound, show the empirical rate against it; show convergence as the grid refines.
- Choose parameters with financial meaning (volatilities, maturities, strikes) so the illustration speaks to the modelling problem.
- Keep numerics subordinate. They support the theory; they are never the contribution. Do not let a numerical section grow into a stand-alone empirical study.
Reproducibility (light but real)
- Pin software/library versions; set and report random seeds for any Monte Carlo.
- Make illustrative code reproducible; consider archiving it (Zenodo/GitHub) and citing it.
- Include a Data Availability Statement even if no external data are used (see mathfin-replication-and-data-policy).
Matching scheme to result type
| Result being illustrated | Natural scheme | What the exhibit must report |
|---|---|---|
| Strong/weak SDE convergence rate | Euler–Maruyama or Milstein with halving steps | log–log error slope against the proven order |
| BSDE well-posedness or rate | Backward Euler / least-squares Monte Carlo / deep BSDE solver | terminal error and driver residual across grids |
| Optimal stopping / free boundary | Binomial tree or PDE variational-inequality solver | boundary location against the smooth-fit characterization |
| Rough-volatility approximation | Hybrid scheme for fractional kernels; Markovian lift | implied-vol skew slope against the proven power law |
| Duality gap = 0 | Primal candidate and dual bound computed independently | gap shrinking as the discretization refines |
| Mean-field limit | N-player simulation vs. McKean–Vlasov solver | distance to the limit decaying in N at the stated rate |
Worked micro-example: convergence exhibit for a rough-volatility paper
Suppose Theorem 3.2 proves that a Markovian multi-factor approximation of a rough volatility model converges at a rate governed by the Hurst parameter H. The journal-appropriate exhibit: simulate both models with the same Brownian increments, plot the implied-volatility error against the number of factors on log axes, draw the theoretical slope as a reference line, and caption with the scheme, step size, path count, seed, and the theorem number. What would NOT fit: calibrating the approximation to index-option data and reporting fit quality — that turns an illustration into the empirical study the journal screens out.
Pre-submission numerics audit
- Every exhibit names the theorem, proposition, or rate it illustrates — no orphan plots.
- The observed rate is computed (regression slope), not eyeballed, and stated next to the proven one.
- Degenerate sanity cases (zero volatility, Black–Scholes limit, H → 1/2) reproduce known closed forms before the general runs are trusted.
- The numerical section would survive deletion: the theorems stand alone without it.
Anti-patterns
- A numerical study with no theorem behind it (out of scope for this journal).
- Plots with no error/convergence analysis where the theory promises a rate.
- Unstated scheme, step size, or path count — irreproducible.
- Calibrating to real market data and presenting it as the paper's result.
Output format
【Experiment】what it illustrates (which theorem/rate)
【Method】scheme + step/paths + variance reduction
【Error reported】empirical vs. theoretical rate/bound
【Parameters】financial values used
【Reproducibility】seeds + versions + code location
【Next step】mathfin-tables-figures
版本历史
- 1839142 当前 2026-07-05 14:04
