Prove2Me

Aggregate funding and deficit amortisation: pfModifiedRate_zero_deficit

Proved
ActuarialValuation.pfModifiedRate_zero_deficit

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

actuarial-sciencedb-funding-experienceformal-verification

At full funding the modified contribution rate equals the normal rate. This original derived actuarial relation uses the parameter restrictions, endpoints and units stated in the separate formal theorem or definition.

Mathematical relation:

ragg=Bx−AxPx,rmodified=rnormal+Lx−Axar_{\text{agg}}=\frac{B_x-A_x}{P_x},\qquad r_{\text{modified}}=r_{\text{normal}}+\frac{L_x-A_x}{a}
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_pfModifiedRate
Formal statement
namespace ActuarialValuation

theorem pfModifiedRate_zero_deficit (normal annuity : ℝ) : pfModifiedRate normal 0 annuity=normal := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 7. Institute and Faculty of Actuaries, GN26 Pension Fund Terminology, §§4.5–4.9, https://www.actuaries.org.uk/system/files/documents/pdf/gn26v2-0.pdf; OECD Working Paper, Funding Rules and Actuarial Methods, §§74–76, https://www.oecd.org/content/dam/oecd/en/publications/reports/2006/10/funding-rules-and-actuarial-methods_g17a1941/274307371724.pdf; Actuarial Standards Board ASOP No.4, https://www.actuarialstandardsboard.org/asops/measuring-pension-obligations-determining-pension-plan-costs-contributions/. Parent topic: Entry age and attained age normal costs, aggregate and modified contributions, deficit amortisation and exact funding-surplus rollforward. 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/gn26v2-0.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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