Prove2Me

Average-cost-per-claim projection and reserve reconciliation: irACPCUltimate_nonneg

Proved
ActuarialValuation.irACPCUltimate_nonneg

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

actuarial-scienceformal-verificationinflation-acpc-reserving

Ultimate cost is nonnegative given nonnegative frequency and severity. This original derived actuarial relation uses the parameter restrictions, endpoints and units stated in the separate formal theorem or definition.

Mathematical relation:

Ui=NiultAiult,Ri=Ui−PiU_i=N_i^{\text{ult}}A_i^{\text{ult}},\quad R_i=U_i-P_i
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_irACPCUltimate
Formal statement
namespace ActuarialValuation

theorem irACPCUltimate_nonneg (count avg : ℝ) (hc : 0≤count) (ha : 0≤avg) : 0≤irACPCUltimate count avg := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 382. Institute and Faculty of Actuaries, High-level Methods for Incorporating Changing Inflation into Claims Reserve Estimates, https://vle.actuaries.org.uk/pluginfile.php/168696/mod_resource/content/1/Reserving%20During%20Volatile%20Inflation%20v1.9.pdf; IFoA Claims Reserving report, https://www.actuaries.org.uk/system/files/documents/pdf/0353-0413.pdf. Parent topic: Inflation-adjusted incremental triangle with calendar-year indices, de-inflation, development and reinflation; claim-frequency and average-cost ultimate reserve reconciliation. 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.actuaries.org.uk/system/files/documents/pdf/0353-0413.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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