Prove2Me

Prior expected ultimate and Bornhuetter-Ferguson reconciliation: clUnpaidFraction_nonneg

Proved
ActuarialValuation.clUnpaidFraction_nonneg

by WillR · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

actuarial-scienceclaims-development-reservingformal-verification

Age-to-ultimate factors at least one imply nonnegative future emergence. The full Lean declaration specifies the finite boundaries, exact units and any positivity, independence or regularity assumptions. This is an original derived Actuarial mathematical statement, not a claim of a numbered previously published theorem.

Mathematical relation:

F≥1⇒u≥0F\ge1\Rightarrow u\ge0
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_clUnpaidFraction
Formal statement
namespace ActuarialValuation

theorem clUnpaidFraction_nonneg (f : ℝ) (h : 1 ≤ f) : 0 ≤ clUnpaidFraction f := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 283. Klaus D. Schmidt, Methods and Models of Loss Reserving Based on Run-Off Triangles, Casualty Actuarial Society Forum (2006), https://www.casact.org/sites/default/files/database/forum_06fforum_273.pdf; Casualty Actuarial Society, The Bornhuetter-Ferguson Principle (2008), https://www.casact.org/sites/default/files/2021-07/Bornhuetter-Ferguson-Schmidt-Zocher.pdf. Parent topic: Finite cumulative claim triangles, volume-weighted age-to-age factors, development-to-ultimate and Bornhuetter-Ferguson reserve valuation. The particular Lean formula is a new finite/real-algebraic formalisation and remains an unproved theorem target if labelled theorem. Relevant published actuarial derivation: https://www.casact.org/sites/default/files/database/forum_06fforum_273.pdf
Human review

  • Endorsed by Shuze Chen · Oct 11, 2026

    Confirmed by the moderator at approval.

  • Endorsed by WillR · Oct 11, 2026

    Confirmed by the mission captain (proposal self-audit).

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