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mathfin-topic-selection

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Use when choosing or sharpening a problem for Mathematical Finance (Wiley) — tests whether the question is a methodologically novel, rigorously tractable contribution to financial modelling (stochastic analysis, pricing, risk, portfolio, microstructure) rather than a routine computational application to data.

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Source SKILL.md: https://github.com/brycewang-stanford/Awesome-Journal-Skills/blob/HEAD/Mathematical-Finance-Skills/skills/mathfin-topic-selection/SKILL.md

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Problem Selection (mathfin-topic-selection)

When to trigger

  • Deciding whether a financial-mathematics idea is a fit for Mathematical Finance
  • Holding a result that might be "just a numerical study" and unsure it clears the bar
  • Choosing between an incremental extension and a genuinely novel modelling contribution

The Mathematical Finance fit bar

Mathematical Finance evaluates submissions on methodological novelty and contribution to financial modelling, presented with full mathematical rigor. The litmus test is not "is this about finance" but "does it advance the mathematics of a financial-modelling problem with a result that needs a proof." Strong topics live in the journal's stochastic-analysis tradition:

  1. New tractable models — e.g., a jump/rough/Lévy or stochastic-volatility model with a provable pricing or hedging characterization.
  2. New structural results — existence/uniqueness, FTAP-type equivalences, duality, verification theorems for control/BSDE problems.
  3. New methods — a transform, free-boundary, mean-field, or stochastic-control technique that solves a previously open financial-modelling problem.
  4. New mathematical objects with financial meaning — risk measures, time-consistency notions, arbitrage concepts with rigorous representation theorems.

Disqualifiers (off-fit)

  • Routine computation on financial data with no supporting rigorous analysis — explicitly not considered by the journal.
  • A purely empirical/econometric finance result (better fit for an empirical finance journal).
  • An incremental special case of a known theorem with no new technique or insight.
  • A model proposed without proofs of its formal properties (the paper must be self-contained, proofs included).

Active-frontier scan (hedged)

Strands with sustained presence in the journal's recent volumes — verify against the latest issues before committing, since frontiers move:

  • robust finance and model uncertainty (non-dominated superhedging, Knightian preferences);
  • rough volatility: approximation theory, short-maturity asymptotics, Markovian lifts;
  • mean-field games and large-population equilibria with financially meaningful constraints;
  • (martingale) optimal transport methods for model-free pricing bounds;
  • equilibrium and price-impact models with frictions; optimal execution theory;
  • dynamic risk measures, time consistency, and capital-allocation representations;
  • term-structure theory beyond classical HJM, including stochastic discontinuities and overnight-rate benchmarks.

A topic on a cold strand still fits if the theorem is strong; a hot strand never excuses a routine corollary.

Tractability stress test

Q1 Can you state the conjectured theorem now, with explicit hypotheses?      no  -> not ready
Q2 Which known machinery carries 80% of the proof?                           none -> high risk
Q3 What is the genuinely new step, in one sentence?                          none -> incremental
Q4 Does a financial quantity (price, hedge, boundary, equilibrium) appear
   in the conclusion, not just the motivation?                               no  -> wrong venue
Q5 Is there a degenerate case you can solve completely first?                yes -> start there

Vignette: choosing between two term-structure problems

Problem A: extend a known HJM consistency theorem from continuous to càdlàg forward curves — statable theorem, identified obstacle (jump measures break the old compactness step), clear payoff (benchmark-rate discontinuities at announcement dates). Problem B: simulate a new three-factor curve model and show it fits swaption smiles. A passes Q1–Q4; B fails Q4's theorem requirement and lands in the journal's explicit out-of-scope zone. Choose A, and scope it by Q5: deterministic jump times first, the general case after.

Sharpening questions

  • What is the theorem, in one sentence, and why is it new?
  • Is the contribution the model, the method, or the result — and is that the novel part?
  • Could a referee from the Bachelier-Finance-Society community see the financial-modelling payoff, not just a math exercise?
  • Are the assumptions general enough to matter, but precise enough to prove?

Output format

【Problem】one sentence
【Type of novelty】model / method / structural result / object
【Core theorem】one sentence (what gets proved)
【Financial-modelling payoff】why it matters for pricing/risk/portfolio/microstructure
【Fit verdict】fit / off-fit + reason
【Next step】mathfin-literature-positioning