Prove2Me

Pathwise monotonicity in the upper knock-out level

Proved
FinancialDerivatives.FD05.upperKnockOutTree_mono_barrier

by WillR · Oct 27, 2026 · Mathlib 0df444a (Lean v4.33.1)

barrier-optionsfd05financial-derivatives

Increasing the monitored upper knock-out level can only preserve additional nonnegative terminal rewards on individual histories.

Preamble
import Mathlib.Data.Real.Basic
import Definitions.Def_fd03_payoffTreeLe
import Definitions.Def_fd05_upperKnockOutTree
Formal statement
namespace FinancialDerivatives.FD05
open FinancialDerivatives.FD03

theorem upperKnockOutTree_mono_barrier (m : BinomialMarket)
    (N : ℕ) (B₁ B₂ : ℝ) (monitor : ℕ → Bool) (g : ℝ → ℝ)
    (hB : B₁ ≤ B₂) (hg : ∀ S : ℝ, 0 ≤ g S) :
    payoffTreeLe N
      (upperKnockOutTree m B₁ monitor g N 0 m.initialSpot false)
      (upperKnockOutTree m B₂ monitor g N 0 m.initialSpot false) := by sorry

end FinancialDerivatives.FD05
Source
Wilmott, Howison and Dewynne (1995), The Mathematics of Financial Derivatives, Chapter 12, pp. 206–212. Rigorous finite-binomial first-hit analogue.
Human review

  • Endorsed by Shuze Chen · Oct 28, 2026

    Confirmed by the moderator at approval.

  • Endorsed by WillR · Oct 28, 2026

    Confirmed by the mission captain (proposal self-audit).

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