Prove2Me

Monitored inception barrier causes immediate extinction

Proved
FinancialDerivatives.FD05.initiallyTouched_knockout_zero

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

barrier-optionsfd05financial-derivatives

If inception is monitored and the initial stock already reaches the upper level, every terminal knock-out claim pays zero.

Preamble
import Mathlib.Data.Real.Basic
import Definitions.Def_fd05_upperKnockOutTree
import Definitions.Def_fd03_europeanValue
Formal statement
namespace FinancialDerivatives.FD05
open FinancialDerivatives.FD03

theorem initiallyTouched_knockout_zero (m : BinomialMarket) (N : ℕ)
    (B : ℝ) (monitor : ℕ → Bool) (g : ℝ → ℝ)
    (hM : monitor 0 = true) (hB : B ≤ m.initialSpot) :
    europeanValue m N
      (upperKnockOutTree m B monitor g N 0 m.initialSpot false) = 0 := 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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