Prove2Me

Pathwise nonnegative knock-out claim is below vanilla

Proved
FinancialDerivatives.FD05.upperKnockOutTree_le_vanilla

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

barrier-optionsfd05financial-derivatives

A nonnegative terminal reward is either retained or extinguished by an upper knock-out barrier, so the payoff is pathwise bounded by vanilla.

Preamble
import Mathlib.Data.Real.Basic
import Definitions.Def_fd03_payoffTreeLe
import Definitions.Def_fd05_upperKnockOutTree
import Definitions.Def_fd05_vanillaTerminalTree
Formal statement
namespace FinancialDerivatives.FD05
open FinancialDerivatives.FD03

theorem upperKnockOutTree_le_vanilla (m : BinomialMarket)
    (N : ℕ) (B : ℝ) (monitor : ℕ → Bool) (g : ℝ → ℝ)
    (hg : ∀ S : ℝ, 0 ≤ g S) :
    payoffTreeLe N (upperKnockOutTree m B monitor g N 0 m.initialSpot false) (vanillaTerminalTree m N g) := 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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