Development to ultimate and outstanding reserve: clUltimate_unit

Proved

ActuarialValuation.clUltimate_unit

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

actuarial-scienceclaims-development-reservingformal-verification

No remaining development makes ultimate equal the latest cumulative paid amount. 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:

U(C,1)=C

Preamble

import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_clUltimate

Formal statement

namespace ActuarialValuation

theorem clUltimate_unit (p : ℝ) : clUltimate p 1 = p := 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).

View graph