Projected service and accrued benefits: pucTotalBenefit_zero
ProvedActuarialValuation.pucTotalBenefit_zeroactuarial-scienceformal-verificationprojected-unit-funding
An empty past and future service ledger has zero pension. 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:
Preamble
import Mathlib.Data.Real.Basic import Mathlib.Algebra.BigOperators.Group.Finset.Basic import Definitions.Def_actuarial_pucTotalBenefit
Formal statement
namespace ActuarialValuation theorem pucTotalBenefit_zero (u : ℕ → ℝ) : pucTotalBenefit u 0 0 = 0 := by sorry end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 5. American Academy of Actuaries, Fundamentals of Pension Accounting and Funding (2004), https://www.actuary.org/sites/default/files/pdf/pension/fundamentals_0704.pdf; IFoA GN26 Pension Fund Terminology (2006), https://www.actuaries.org.uk/system/files/documents/pdf/gn26v2-1.pdf; IMF, Conducting Stress Tests of Defined Benefit Pension Plans (2014), https://www.elibrary.imf.org/display/book/9781484368589/ch012.xml. Parent topic: Projected unit credit pension funding, service attribution, normal cost, actuarial liability and amortisation of unfunded pension liabilities. 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.actuary.org/sites/default/files/pdf/pension/fundamentals_0704.pdf
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.