Prove2Me

Absorbing backward recursion equals full-tree European valuation

Proved
FinancialDerivatives.FD05.upperKnockOut_eq_absorbing

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

barrier-optionsfd05financial-derivatives

The independently defined absorbing recursion produces exactly the FD-03 European price of the full-path upper knock-out terminal claim.

Preamble
import Mathlib.Data.Real.Basic
import Definitions.Def_fd05_upperKnockOutTree
import Definitions.Def_fd05_upperAbsorbingValue
import Definitions.Def_fd03_europeanValue
Formal statement
namespace FinancialDerivatives.FD05
open FinancialDerivatives.FD03

theorem upperKnockOut_eq_absorbing (m : BinomialMarket) (N : ℕ)
    (B : ℝ) (monitor : ℕ → Bool) (g : ℝ → ℝ) :
    upperAbsorbingValue m B monitor g N 0 m.initialSpot false =
      europeanValue m N
        (upperKnockOutTree m B 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).

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