mathfin-contribution-framing

Contribution Framing (mathfin-contribution-framing)

When to trigger

• The math is correct but the introduction does not say why it advances financial modelling
• A referee might ask "this is rigorous, but what is the new modelling insight?"
• Reviewing whether the stated contribution matches what the theorems actually deliver

The Mathematical Finance contribution bar

The journal evaluates papers on methodological novelty and contribution to financial modelling. Rigor is necessary but not sufficient: a correct theorem with no modelling payoff reads as a math paper sent to the wrong venue, while a modelling claim without proof reads as informal finance. The contribution must be both mathematically novel and consequential for a financial-modelling problem (pricing, hedging, risk measurement, portfolio choice, optimal execution, arbitrage theory).

How to frame the contribution

1. Lead with the modelling problem, then the obstruction prior methods hit, then your theorem as the resolution.
2. Name the novelty axis explicitly: a new tractable model, a weaker assumption set, a constructive solution where only existence was known, a sharper rate/bound, a new representation (e.g., of a risk measure), or a unifying framework.
3. Translate the theorem into a modelling statement: "hence the option price solves...", "hence the optimal strategy is...", "hence the risk measure admits the representation..."
4. Bound the claim to the hypotheses — state where the result holds and where it does not, consistent with the rigor culture (over-claiming is penalized).
5. Place numerics in service of the claim: if you include experiments, frame them as illustrating the theorem (convergence, qualitative behavior), never as the contribution itself — routine computation on data is out of scope.

Novelty-axis evidence table

For each novelty axis the introduction must put specific evidence on the page; referees test the claim against the theorem statements themselves:

Novelty axis	What the introduction must show	How a referee tests it
New tractable model	The closed-form or characterizing equation (PDE/BSDE/transform) the model admits	Re-derive the characterization from the stated dynamics
Weaker assumption set	The exact hypothesis removed (e.g., no dominating measure, unbounded coefficients)	Search the proof for a hidden reinstatement of the dropped condition
Constructive solution	The object built (optimal strategy, hedging portfolio, stopping boundary)	Check the construction is admissible and attains the value
Sharper rate/bound	Old rate vs. new rate, with the regime where the gain bites	Compare against known lower bounds or counterexamples
New representation	The dual/variational formula and the space it lives on	Verify both inequalities of the duality, not just one
Unifying framework	At least two prior results recovered as corollaries	Confirm the corollaries follow without extra hypotheses

Worked vignette: a robust superhedging paper

Hypothetical manuscript: pathwise superhedging duality for path-dependent claims under volatility uncertainty. Applying the framing rules:

• 【Modelling problem】price and superhedge a claim when no single probabilistic model is trusted.
• 【Obstruction】classical duality needs a reference measure; under non-dominated uncertainty the martingale measures are mutually singular, so measurable-selection and capacity issues block the standard argument.
• 【Theorem as resolution】duality between the cheapest superhedge and the supremum of martingale expectations holds for upper semicontinuous claims, with dual attainment.
• 【Novelty axis】weaker assumption set (no dominating measure) plus a new representation.
• 【Modelling payoff】robust price bounds and an explicit hedge that works model-free.
• 【Scope of claim】upper semicontinuity is essential; the introduction says so and points to the counterexample section.

Calibration against accepted introductions

Accepted Mathematical Finance papers typically open in one to two pages: modelling problem and obstruction in the first paragraphs, the main theorem stated informally (or by number) by page two, a short literature paragraph keyed to assumptions, then a roadmap. Long motivational essays are rare; so are introductions that postpone the main result past the model setup. When unsure of current norms, calibrate against the latest issues rather than older volumes.

Anti-patterns

• A theorem-dump introduction with no modelling "so what."
• Claiming practical/empirical impact the paper does not establish.
• Selling generality the proofs do not support.
• Framing numerical results as the core contribution.
• Burying the actual novelty under restated background.

Output format

【Modelling problem】one sentence
【Obstruction in prior work】what prevented it
【Theorem as resolution】one sentence
【Novelty axis】model / assumption / constructive / rate / representation / unification
【Modelling payoff】the financial statement the theorem licenses
【Scope of claim】where it holds / does not
【Next step】mathfin-data-analysis (if numerics) or mathfin-writing-style