Entry age, attained age and liability allocation: pfEntryCost_zero_salary
ProvedActuarialValuation.pfEntryCost_zero_salaryactuarial-sciencedb-funding-experienceformal-verification
The level-payroll normal cost vanishes at zero salary. This original derived actuarial relation uses the parameter restrictions, endpoints and units stated in the separate formal theorem or definition.
Mathematical relation:
Preamble
import Mathlib.Data.Real.Basic import Mathlib.Algebra.BigOperators.Group.Finset.Basic import Definitions.Def_actuarial_pfEntryNormalCost
Formal statement
namespace ActuarialValuation theorem pfEntryCost_zero_salary (rate : ℝ) : pfEntryNormalCost rate 0=0 := 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
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.