Prove2Me

Knock-out value increases with an upper barrier

Proved
FinancialDerivatives.FD05.upperKnockOut_price_mono_barrier

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

barrier-optionsfd05financial-derivatives

For nonnegative terminal rewards, raising an upper knock-out level weakly increases survival and the risk-neutral option value.

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 upperKnockOut_price_mono_barrier (m : BinomialMarket)
    (N : ℕ) (B₁ B₂ : ℝ) (monitor : ℕ → Bool) (g : ℝ → ℝ)
    (hB : B₁ ≤ B₂) (hg : ∀ S : ℝ, 0 ≤ g S) :
    europeanValue m N
      (upperKnockOutTree m B₁ monitor g N 0 m.initialSpot false) ≤
    europeanValue m N
      (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).

View graph