Prove2Me

Residual dispersion and one-step uncertainty: mackSquaredResidual_zero

Proved
ActuarialValuation.mackSquaredResidual_zero

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

actuarial-scienceformal-verificationmack-reserve-variability

Perfect fitted development contributes no squared residual. 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:

e(C,C)2=0e(C,C)^2=0
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_mackSquaredResidual
Formal statement
namespace ActuarialValuation

theorem mackSquaredResidual_zero (actual : ℝ) : mackSquaredResidual actual actual = 0 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 213. Thomas Mack (1993), Distribution-free Calculation of the Standard Error of Chain Ladder Reserve Estimates, ASTIN Bulletin 23(2), pp. 213-225, https://www.casact.org/sites/default/files/database/astin_vol23no2_213.pdf; Thomas Mack (1999), The Standard Error of Chain Ladder Reserve Estimates: Recursive Calculation and Inclusion of a Tail Factor, https://www.casact.org/sites/default/files/database/astin_vol29no2_361.pdf. Parent topic: Mack claims reserving uncertainty, finite conditional development factor moments, process variance and estimation uncertainty. 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/astin_vol23no2_213.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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