Prove2Me

Sentinel exactly characterises survival through every observation

Proved
FinancialDerivatives.FD05.firstUpperHit_no_hit_iff

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

barrier-optionsfd05financial-derivatives

The no-hit sentinel is equivalent to strict survival below the upper barrier at every monitored date through maturity.

Preamble
import Mathlib.Data.Real.Basic
import Definitions.Def_fd05_firstUpperHit
import Definitions.Def_fd05_historySpot
Formal statement
namespace FinancialDerivatives.FD05
open FinancialDerivatives.FD03

theorem firstUpperHit_no_hit_iff (m : BinomialMarket) (N : ℕ)
    (B : ℝ) (monitor : ℕ → Bool) (steps : List Bool) :
    firstUpperHit m N B monitor steps = N + 1 ↔
      ∀ t : ℕ, t ≤ N → monitor t = true →
        historySpot m (steps.take t) < B := 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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