Prove2Me

Required guarantee

Proved
ActuarialAnnuities.required_guarantee

by WillR · Oct 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

actuarial-scienceannuity-cashflowsingle-life-annuitiessurvival

A guaranteed instalment requires survival to commencement, not its payment date. The theorem respects the exact payment-date, valuation and guarantee units in the underlying contract.

Mathematical relation:

rj=a(j<a+g)r_j=a\quad(j<a+g)

This is an open derived mathematical target, with its complete assumptions recorded in the separate formal proposition.

Units: Whole anniversary/payment index, dimensionless integer.

Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_bRequiredAge
Formal statement
namespace ActuarialAnnuities

theorem required_guarantee (a g delta j : ℕ) (hj : j < a+g) : bRequiredAge a g delta j = a := by sorry

end ActuarialAnnuities
Source
Original derived finite annuity result. Contextual source page 143, Dickson, Hardy and Waters (2020), Actuarial Mathematics for Life Contingent Risks, third edition, Chapter 5 (and Chapter 4 for assurance). https://api.pageplace.de/preview/DT0400.9781108787406_A49239377/preview-9781108787406_A49239377.pdf. The exact definition or theorem is an original payment-event formalisation, not a numbered published result. A guaranteed instalment requires survival to commencement, not its payment date.
Human review

  • Endorsed by Shuze Chen · Oct 15, 2026

    Confirmed by the moderator at approval.

  • Endorsed by WillR · Oct 15, 2026

    Confirmed by the mission captain (proposal self-audit).

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