Prove2Me

Prior expected ultimate and Bornhuetter-Ferguson reconciliation: clPaidFraction_nonneg

Proved
ActuarialValuation.clPaidFraction_nonneg

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

actuarial-scienceclaims-development-reservingformal-verification

The developed fraction is nonnegative for positive age-to-ultimate development. 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>0⇒w≥0F>0\Rightarrow w\ge0
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_clPaidFraction
Formal statement
namespace ActuarialValuation

theorem clPaidFraction_nonneg (f : ℝ) (h : 0 < f) : 0 ≤ clPaidFraction 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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