Prove2Me

Connect recursive tree weights with explicit surviving-history weights

Proved
FinancialDerivatives.FD05.weightedPathSum_knockOut_survival

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

barrier-optionsfd05financial-derivatives

FD-03's recursively weighted payoff-tree valuation of a knock-out contract agrees after discounting with the FD-05 explicit full-history first-hit sum.

Preamble
import Mathlib.Data.Real.Basic
import Definitions.Def_fd03_weightedPathSum
import Definitions.Def_fd05_upperKnockOutTree
import Definitions.Def_fd05_discountedSurvivalPathPrice
Formal statement
namespace FinancialDerivatives.FD05
open FinancialDerivatives.FD03

theorem weightedPathSum_knockOut_survival (m : BinomialMarket)
    (N : ℕ) (B : ℝ) (monitor : ℕ → Bool) (g : ℝ → ℝ) :
    weightedPathSum m N (upperKnockOutTree m B monitor g N 0 m.initialSpot false) / m.growth ^ N =
      discountedSurvivalPathPrice m N B monitor 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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