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