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mathfin-identification-strategy
GitHub针对《Mathematical Finance》期刊的数学严谨性检查技能，聚焦假设精确性、定理陈述及证明架构。用于识别模型漏洞、验证无套利条件及确保自包含证明，适用于定价、随机控制等理论场景。
Trigger Scenarios
模型形式性质未证明
假设模糊不清
证明存在逻辑缺口或循环论证
不确定贡献的通用性程度
Install
npx skills add brycewang-stanford/Awesome-Journal-Skills --skill mathfin-identification-strategy -g -y
SKILL.md
Frontmatter
{
"name": "mathfin-identification-strategy",
"description": "Use when the mathematical core of a Mathematical Finance (Wiley) manuscript is the bottleneck — adapted for a theory journal, this means assumptions, theorem statements, proof architecture, and generality, not causal\/empirical identification. Stress-tests rigor before exposition is polished."
}
Assumptions, Theorems & Proof Architecture (mathfin-identification-strategy)
Note on framing
Mathematical Finance is a theory-first journal: papers are evaluated on methodological novelty and rigor, not empirical causal identification. The "identification" that matters here is mathematical identification — pinning down the right assumptions, the precise theorem, and a complete proof. This skill therefore covers assumptions, results, proof exposition, and generality. (Empirical causal design is out of scope for this venue.)
When to trigger
- A "model" is proposed but its formal properties (existence, uniqueness, no-arbitrage) are unproved
- The assumptions are vague (which filtration? which integrability? which regularity?)
- A proof has a gap, an unstated measurability/integrability condition, or a circular step
- You are unsure your generality is the right level for the contribution
The rigor bar (the journal requires self-contained full proofs)
- State assumptions precisely. Probability space, filtration and its conditions (usual conditions?), integrability ($L^p$, square-integrability), regularity, market structure (complete/incomplete), admissibility of strategies. Number them (A1, A2, ...) and reuse them.
- State the theorem cleanly. Hypotheses → conclusion, with the object's existence, uniqueness, and characterization separated. Avoid burying conditions in prose.
- Make the proof self-contained. Full proofs of all formal results are required; cite external theorems with exact hypotheses and check they apply (e.g., that a martingale is genuinely a martingale, not just a local one).
- Get the generality right. Too narrow → looks like a special case (see mathfin-literature-positioning); too broad → the proof breaks. Justify each assumption: is it essential, or a convenience that could be relaxed?
- Guard the standard pitfalls. Local vs. true martingale, integrability of stochastic integrals, applicability of Itô / Girsanov / Feynman–Kac, well-posedness of SDEs/BSDEs, verification of HJB solutions, smooth-fit at free boundaries, NFLVR/FTAP conditions.
Branch paths
- Pricing / no-arbitrage: establish the (equivalent) martingale measure; verify NFLVR / FTAP hypotheses; confirm the discounted price is a true martingale.
- Stochastic control / portfolio: state the HJB / verification theorem; check admissibility and the transversality/integrability conditions; prove the candidate is optimal, not just stationary.
- BSDE / duality: existence–uniqueness under stated drivers; comparison theorem if used; rigorous duality gap = 0 argument.
- Optimal stopping / free boundary: Snell envelope or variational inequality; smooth-pasting justified, not assumed.
Assumption-block and statement templates
A house-style assumption block fixes the stochastic basis once and lets every result refer to it by label:
\begin{assumption}\label{ass:basis}
$(\Omega,\mathcal F,(\mathcal F_t)_{t\in[0,T]},\mathbb P)$ is a filtered probability space
satisfying the usual conditions and supporting a $d$-dimensional Brownian motion $W$.
\end{assumption}
\begin{assumption}\label{ass:coeff}
$b,\sigma$ are progressively measurable; $\sigma\sigma^{\top}$ is uniformly elliptic and
$\mathbb E\!\int_0^T \big(|b_t|^2 + |\sigma_t|^4\big)\,dt < \infty$.
\end{assumption}
\begin{theorem}\label{thm:main}
Under Assumptions \ref{ass:basis}--\ref{ass:coeff}, the value function ... Moreover, the
optimal strategy $\pi^{\star}$ is admissible and unique up to indistinguishability.
\end{theorem}
Separating the basis assumption from the coefficient assumption lets you weaken one without touching results that need only the other — referees notice and reward this modularity.
Where each lemma lives
- Main text: the lemma carrying the new idea (a novel estimate, a new compactness or selection argument) — referees should meet it before the main proof, with a sentence saying why existing estimates fail.
- Appendix: routine verifications (moment bounds, measurability of value functions, standard localization steps) — each still proved in full, never waved at.
- Inline remark: one-line consequences of cited results, with the citation pinned to the exact theorem number and a sentence confirming its hypotheses hold here.
- Never split one proof across main text and appendix mid-argument: give a sketch in the text and defer the complete proof as a single unit.
Anti-patterns
- "It is well known that..." standing in for a required step.
- Assuming an integrability/measurability condition only where convenient.
- Treating a local martingale as a martingale without a uniform-integrability argument.
- Stating maximal generality the proof cannot support.
- Relegating a load-bearing lemma to "the reader can verify."
Output format
【Main theorem】hypotheses → conclusion (one line)
【Assumptions】[A1, A2, ...] with role of each
【Proof architecture】lemmas → main steps → where external theorems enter
【Generality check】each assumption: essential / relaxable
【Pitfalls cleared】[martingale, integrability, well-posedness, smooth-fit, ...]
【Gaps remaining】[...]
【Next step】mathfin-contribution-framing
Version History
- 1839142 Current 2026-07-05 14:04
