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.

1. Assumption scope: too strong, too weak, unstated, or not financially interpretable.
2. Novelty: overlap with prior theorem, special-case concern, missing citation.
3. Financial modelling relevance: theorem correct but payoff unclear.
4. 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