mathfin-tables-figures

Tables & Figures (mathfin-tables-figures)

When to trigger

• A numerical section needs figures or tables
• A proof-heavy manuscript needs diagrams, assumption maps, or appendix organization
• Exhibits risk looking like empirical finance rather than theorem support

Exhibit rules

Every exhibit should answer: which theorem, proposition, algorithm, or modelling

insight does this support?

1. Tie figures to formal results. A convergence plot should cite the theorem or

rate it illustrates.

1. Report numerical settings. Grid, time step, paths, tolerance, truncation,

seed, and software version belong in the caption or appendix.

1. Keep tables small. Use them for parameter values, convergence rates,

boundary comparisons, or sensitivity to assumptions.

1. Move detail to appendices. The author guidelines encourage detailed

mathematical analysis in appendices; use them for long derivations and

extended numerical diagnostics.

1. Avoid empirical-style claims. A calibration illustration does not establish

an empirical result unless the paper is designed for that, which this venue

generally is not.

Good exhibits

• Error decay against the proven rate
• Free-boundary shape implied by an optimal stopping theorem
• Sensitivity of a pricing formula to parameters with financial meaning
• Algorithm pseudocode paired with convergence conditions
• Assumption dependency diagram for a complex theorem

Theorem-dependency map as an exhibit

For a paper with layered results, a compact dependency table orients referees faster than

prose:

Assumptions:  (A1) filtered space, usual conditions   (A2) NFLVR   (A3) bounded volatility
Lemma 3.1   <- (A1),(A2)       uniform integrability of the deflated wealth process
Lemma 3.2   <- (A1),(A3)       gradient bound for the value function
Theorem 4.1 <- L3.1, L3.2      duality and existence of the optimizer
Theorem 4.2 <- Thm 4.1,(A3)    regularity of the free boundary

Place it at the end of the introduction or the head of the proofs section; it doubles as your

own audit that no result silently uses an unlisted assumption.

Figure axes speak the model's notation

• Label axes with the manuscript's symbols (t, S_t, the boundary b(t), the Hurst index H), not

plotting-library defaults — a referee matching the plot to Theorem 4.2 should never have to

translate notation.

• State units only where financially meaningful (years to maturity, volatility in annual

terms); pure mathematical objects need no units.

• If a curve depends on a parameter the theorem restricts, show only values inside the

theorem's hypotheses, or mark excursions outside them explicitly as such.

Algorithm displays

Pseudocode earns its place only when the paper proves something about the algorithm

(convergence, complexity, stability). Pair each algorithm float with the statement number of

that guarantee, keep inputs and outputs in the manuscript's notation, and state the stopping

criterion explicitly — referees check that the displayed loop matches the object analyzed in

the proof, not a simplified cousin of it.

Caption rewrite micro-example

A draft caption for an American-put exhibit reads "Exercise boundary for different

volatilities." Journal-ready version: "Free boundary b(t) of the American put under

Assumptions (A1)–(A3), computed with the penalized PDE scheme of Section 5 (grid 400×400,

tolerance 1e-8), illustrating the monotonicity proved in Theorem 4.2; sigma in {0.2, 0.3,

0.4}, r = 0.02, K = 100. The figure illustrates the theorem's qualitative content and makes no

calibration claim." Every clause does one caption-contract job: result, financial object,

settings, interpretation limit.

Caption contract

Each caption should state four things: the formal result illustrated, the financial object, the numerical

settings, and the interpretation limit. For example, a pricing-sensitivity figure should not claim broad

empirical validation; it should say which theorem or model implication the curve helps readers understand.

If the exhibit cannot name a theorem, proposition, or modelling implication, cut it or move it to an

exploratory appendix. Mathematical Finance exhibits are evidence for theory comprehension, not substitutes

for proof.

Output format

[Exhibit] figure / table / algorithm / appendix
[Formal result supported] theorem/proposition/lemma
[Numerical details needed] ...
[Caption claim] ...
[Next step] mathfin-writing-style