Prove2Me

An activated knock-out state has zero continuation value

Proved
FinancialDerivatives.FD05.upperAbsorbingValue_hit

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

barrier-optionsfd05financial-derivatives

Once the knock-out flag records a prior barrier touch, the independently defined recursion has zero value at every remaining maturity.

Preamble
import Mathlib.Data.Real.Basic
import Definitions.Def_fd05_upperAbsorbingValue
Formal statement
namespace FinancialDerivatives.FD05
open FinancialDerivatives.FD03

theorem upperAbsorbingValue_hit (m : BinomialMarket) (B : ℝ)
    (monitor : ℕ → Bool) (g : ℝ → ℝ)
    (n t : ℕ) (S : ℝ) :
    upperAbsorbingValue m B monitor g n t S true = 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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