Prove2Me

Incremental triangles and cumulative development: irRealReserve_positive

Proved
ActuarialValuation.irRealReserve_positive

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

actuarial-scienceformal-verificationinflation-acpc-reserving

Sufficient projected ultimate value gives nonnegative outstanding reserve. This original derived actuarial relation uses the parameter restrictions, endpoints and units stated in the separate formal theorem or definition.

Mathematical relation:

Ci,j=∑k=0jXi,k,Ui=Ci,jfjC_{i,j}=\sum_{k=0}^{j}X_{i,k},\quad U_i=C_{i,j}f_j
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_irRealReserve
Formal statement
namespace ActuarialValuation

theorem irRealReserve_positive (ultimate paid : ℝ) (h : paid≤ultimate) : 0≤irRealReserve ultimate paid := 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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