Mathfin rebuttal

R&R Rebuttal (mathfin-rebuttal)

When to trigger

• A revision decision arrives from Mathematical Finance
• Referees identify proof gaps, unclear assumptions, missing novelty, or weak financial interpretation
• You need a point-by-point response letter and aligned manuscript edits

Triage categories

1. Proof correctness: missing lemma, invalid theorem application, local/true martingale issue, integrability, measurability, boundary condition.
2. Assumption scope: too strong, too weak, unstated, or not financially interpretable.
3. Novelty: overlap with prior theorem, special-case concern, missing citation.
4. Financial modelling relevance: theorem correct but payoff unclear.
5. Exposition: notation, definitions, appendix navigation, numerical explanation.

Response strategy

• Fix proof gaps directly; do not argue around them.
• When an assumption cannot be relaxed, explain why it is necessary and what it means financially.
• If novelty is questioned, compare theorem-by-theorem with the closest prior work.
• Add financial interpretation after formal statements, not only in the introduction.
• Move long derivations to appendices and point referees to exact page/line numbers.

Objection-to-repair map

Referee objection (typical phrasing)	Likely root cause	Repair that satisfies this venue
"X is only a local martingale"	Missing uniform-integrability / Novikov-type condition	Add the integrability lemma; or weaken the conclusion to supermartingale and fix downstream claims
"Girsanov/Itô applied without checking hypotheses"	Cited theorem's conditions were not checked in your setting	Insert a verification step with explicit moment bounds, citing the precise theorem number
"The candidate strategy is not shown admissible"	Admissible set defined too loosely	Tighten the definition, prove membership, re-run the verification theorem
"This follows from [prior work] by a change of variables"	Novelty gap	Theorem-by-theorem comparison; isolate the hypothesis prior work cannot drop
"The proof of Lemma k is only sketched"	Routine step left informal	Write it out in the appendix; never answer with "standard"
"Where is the financial content?"	Payoff stated only in the abstract	Add interpretation remarks after each main theorem

When the referee exhibits a counterexample

Treat a counterexample as data about your hypotheses, not as an attack. First reproduce it and check whether it satisfies your stated assumptions. If it does, the theorem is wrong as stated: find the minimal additional hypothesis that excludes it, restate the result, and say plainly in the letter that the referee found a genuine gap. If it does not, show precisely which labelled assumption it violates and thank the referee for prompting a clarifying remark in the text. Disputing a correct counterexample is the fastest route to rejection at a journal whose referees verify arguments line by line.

Worked vignette: defending a boundedness assumption

A referee asks why volatility is assumed bounded in a term-structure stability theorem and suggests relaxing it. Response options, in descending strength: (1) relax it — prove the result under linear growth plus a moment condition, if the localization survives; (2) keep it but show necessity — exhibit an unbounded-volatility example where the conclusion fails; (3) keep it as a convenience — state exactly which step uses it (a uniform estimate feeding a compactness argument), explain why relaxation needs genuinely new tools, and record it as an explicit open problem. Option 3 is acceptable at this venue only with the precise pointer to the step.

Letter mechanics for a proofs journal

• Quote each comment verbatim, respond beneath it, and give page/equation/label coordinates for every change — referees re-verify proofs and need exact targets.
• Where a proof changed, summarize the new argument in two sentences in the letter so the referee can decide whether to re-read the full appendix.
• List any changes made beyond the referees' requests (renumbered assumptions, notation fixes) so nothing in the diff looks unexplained.
• Keep mathematical disagreement impersonal: counter with a lemma or a reference, never with an appeal to authority.

Response paragraph pattern

We thank the referee for identifying this issue. We have revised [theorem/lemma/
assumption] on page X and added [proof/detail] in Appendix Y. The revised argument
now verifies [condition], which is required for [external theorem/result]. We also
added a paragraph explaining the financial interpretation of this assumption.

Output format

[Decision type] major / minor
[Core mathematical issues] ...
[New proof work] ...
[Novelty clarification] ...
[Financial interpretation added] ...
[Next step] revise manuscript + response letter