Prove2Me

Micro terminal survival

Proved
ActuarialAnnuities.micro_terminal_survival

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

actuarial-scienceannuity-cashflowfractionalsingle-life-annuities

Survival after the last right-censored subperiod vanishes in the finite construction. The theorem respects the exact payment-date, valuation and guarantee units in the underlying contract.

Mathematical relation:

q>hm⇒S(m)(q)=0q>hm\Rightarrow S^{(m)}(q)=0

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

Units: Probability, dimensionless, indexed in whole micro-instalments.

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

theorem micro_terminal_survival (h m q : ℕ) (p : ℕ → ℝ) (hm : 0 < m) (hq : h*m < q) : bUDDMicroSurvival h m p q = 0 := by sorry

end ActuarialAnnuities
Source
Original derived finite annuity result. Contextual source page 152, 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. Survival after the last right-censored subperiod vanishes in the finite construction.
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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