Writing Style (mathfin-writing-style)
When to trigger
- The proofs are correct but the paper is hard to read
- The introduction states results without financial modelling intuition
- Definitions, assumptions, theorem numbering, or appendix references are inconsistent
Style principles
- Define before use. Probability space, filtration, admissible strategies,
integrability, market model, and payoff objects must be explicit.
- Number assumptions and results. Reuse labels consistently.
- State theorem scope precisely. Hypotheses and conclusions should be visible
without searching prose.
- Separate intuition from proof. Give financial meaning before technical proof,
then keep the proof self-contained.
- Use appendices deliberately. Put long derivations there while keeping the
main text focused on result, intuition, and modelling payoff.
Theorem paragraph pattern
Under Assumptions (A1)-(A3), Theorem 2.1 establishes [formal result]. In financial
terms, this means [pricing/hedging/risk/portfolio interpretation]. The proof
combines [main tools] and is given in [location].
Proof hygiene
- Check local martingale versus true martingale claims.
- State integrability and measurability conditions.
- Do not cite a theorem without verifying its hypotheses.
- Avoid "straightforward" for load-bearing steps.
- Keep notation stable across the main text and appendix.
Symbol conventions the readership expects
| Object |
Conventional usage |
Drift to avoid |
| Filtration |
(F_t) with the usual conditions stated once |
switching between F_t and F(t) |
| Physical / pricing measure |
P / Q (or Q^*) |
reusing Q for a generic measure mid-paper |
| Brownian motion |
W under P; W^Q after Girsanov |
the same W under both measures without comment |
| Admissible strategies |
A or A(x), x the initial wealth |
"admissible" used before A is defined |
| Wealth / value process |
X^pi or V |
V doubling as value function and value process |
| Value function |
v(t,x), lowercase |
v and V swapped between sections |
| Stopping times |
tau, ranging over a defined family T_{t,T} |
tau ranging over an unspecified set |
| Generator |
L (or L^a in control problems) |
applying L to functions outside its stated domain |
Proof-sketch scaffold
Before each long proof, give a three-to-five sentence sketch:
The proof proceeds in three steps. Step 1 establishes [a priori estimate] under (A2), which
yields the uniform integrability needed later. Step 2 constructs the candidate [object] via
[tool: Snell envelope / dual problem / fixed point]; this is where the new idea, [one phrase],
enters. Step 3 verifies optimality and uniqueness by [verification argument]. Steps 1 and 3
are standard given Step 2 and are deferred to Appendix B.
The sketch tells a referee where the novelty lives and which parts may be verified quickly —
exactly the separation of new idea from routine verification that this journal's culture
prizes.
Sentence-level habits for stochastic-analysis prose
- Quantify every "small", "sufficiently regular", or "for t large" with a displayed condition.
- Write "P-a.s." or "for Lebesgue-a.e. t" — never leave the null-set sense ambiguous.
- Prefer "By Theorem 2.3 of [X], whose hypotheses hold by (A1) and Lemma 3.2," to a bare
citation.
- Keep proofs in one tense (present), and let displayed equations carry the algebra, not prose.
Notation ledger
Before polishing prose, create a notation ledger with columns for symbol, object, first definition,
assumptions, theorem use, and appendix use. Use it to find:
- one symbol used for multiple objects;
- objects introduced only inside proofs but needed in theorem statements;
- filtrations, measures, admissible sets, or payoff spaces that change silently;
- assumptions cited in prose but absent from the theorem statement;
- appendix notation that no longer matches the main text after revision.
Mathematical Finance readers will forgive technical density more readily than notation drift. A clean
ledger also shortens referee response time because every objection can be tied to a labelled object.
Output format
[Section] intro / model / theorem / proof / numerics / appendix
[Main clarity issue] ...
[Formal precision fix] ...
[Financial intuition fix] ...
[Next step] mathfin-submission
Source: brycewang-stanford/Awesome-Journal-Skills → Mathematical-Finance-Skills/skills/mathfin-writing-style/SKILL.md
1---2name: mathfin-writing-style3description: Use when polishing a Mathematical Finance (Wiley) manuscript's theorem-first exposition — definitions, numbered assumptions, theorem statements, proof sketches, appendices, notation discipline for a stochastic-analysis readership, numerical-experiment prose, and the financial-modelling intuition that accompanies each formal result.4---567# Writing Style (mathfin-writing-style)89## When to trigger1011- The proofs are correct but the paper is hard to read12- The introduction states results without financial modelling intuition13- Definitions, assumptions, theorem numbering, or appendix references are inconsistent1415## Style principles1617- **Define before use.** Probability space, filtration, admissible strategies,18 integrability, market model, and payoff objects must be explicit.19- **Number assumptions and results.** Reuse labels consistently.20- **State theorem scope precisely.** Hypotheses and conclusions should be visible21 without searching prose.22- **Separate intuition from proof.** Give financial meaning before technical proof,23 then keep the proof self-contained.24- **Use appendices deliberately.** Put long derivations there while keeping the25 main text focused on result, intuition, and modelling payoff.2627## Theorem paragraph pattern2829```text30Under Assumptions (A1)-(A3), Theorem 2.1 establishes [formal result]. In financial31terms, this means [pricing/hedging/risk/portfolio interpretation]. The proof32combines [main tools] and is given in [location].33```3435## Proof hygiene3637- Check local martingale versus true martingale claims.38- State integrability and measurability conditions.39- Do not cite a theorem without verifying its hypotheses.40- Avoid "straightforward" for load-bearing steps.41- Keep notation stable across the main text and appendix.4243## Symbol conventions the readership expects4445| Object | Conventional usage | Drift to avoid |46| --- | --- | --- |47| Filtration | (F_t) with the usual conditions stated once | switching between F_t and F(t) |48| Physical / pricing measure | P / Q (or Q^*) | reusing Q for a generic measure mid-paper |49| Brownian motion | W under P; W^Q after Girsanov | the same W under both measures without comment |50| Admissible strategies | A or A(x), x the initial wealth | "admissible" used before A is defined |51| Wealth / value process | X^pi or V | V doubling as value function and value process |52| Value function | v(t,x), lowercase | v and V swapped between sections |53| Stopping times | tau, ranging over a defined family T_{t,T} | tau ranging over an unspecified set |54| Generator | L (or L^a in control problems) | applying L to functions outside its stated domain |5556## Proof-sketch scaffold5758Before each long proof, give a three-to-five sentence sketch:5960```text61The proof proceeds in three steps. Step 1 establishes [a priori estimate] under (A2), which62yields the uniform integrability needed later. Step 2 constructs the candidate [object] via63[tool: Snell envelope / dual problem / fixed point]; this is where the new idea, [one phrase],64enters. Step 3 verifies optimality and uniqueness by [verification argument]. Steps 1 and 365are standard given Step 2 and are deferred to Appendix B.66```6768The sketch tells a referee where the novelty lives and which parts may be verified quickly —69exactly the separation of new idea from routine verification that this journal's culture70prizes.7172## Sentence-level habits for stochastic-analysis prose7374- Quantify every "small", "sufficiently regular", or "for t large" with a displayed condition.75- Write "P-a.s." or "for Lebesgue-a.e. t" — never leave the null-set sense ambiguous.76- Prefer "By Theorem 2.3 of [X], whose hypotheses hold by (A1) and Lemma 3.2," to a bare77 citation.78- Keep proofs in one tense (present), and let displayed equations carry the algebra, not prose.7980## Notation ledger8182Before polishing prose, create a notation ledger with columns for symbol, object, first definition,83assumptions, theorem use, and appendix use. Use it to find:8485- one symbol used for multiple objects;86- objects introduced only inside proofs but needed in theorem statements;87- filtrations, measures, admissible sets, or payoff spaces that change silently;88- assumptions cited in prose but absent from the theorem statement;89- appendix notation that no longer matches the main text after revision.9091Mathematical Finance readers will forgive technical density more readily than notation drift. A clean92ledger also shortens referee response time because every objection can be tied to a labelled object.9394## Output format9596```text97[Section] intro / model / theorem / proof / numerics / appendix98[Main clarity issue] ...99[Formal precision fix] ...100[Financial intuition fix] ...101[Next step] mathfin-submission102```103104---105106**Source:** [`brycewang-stanford/Awesome-Journal-Skills`](https://github.com/brycewang-stanford/Awesome-Journal-Skills) → `Mathematical-Finance-Skills/skills/mathfin-writing-style/SKILL.md`
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