Prove2Me

Annuity-only reduction

Proved
actuarial_d_zero_total_claims

by WillR · Oct 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

actuarial-sciencejoint-lifelife-contingencymultiple-lives

Annuity-only reduction. Suppressing all death riders leaves the member-and-spouse annuity from the same joint law. The settlement date, survivor entitlement, financial discount and relevant joint-law assumptions are those declared in the formal model.

Mathematical relation:

Vtotal;f=s=fx=fy=ft=0=ax+ρay∣xV_{\text{total};f=s=f_x=f_y=f_t=0}=a_x+\rho a_{y\mid x}
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_d_totalValue
import Definitions.Def_actuarial_d_totalPath
import Definitions.Def_actuarial_d_annMemberSpouse
import Definitions.Def_actuarial_d_expect

open ActuarialJointD
Formal statement
theorem actuarial_d_zero_total_claims (h n : ℕ) (p : ℕ → ℕ → ℝ) (d b : ℕ → ℝ) (rho : ℝ) : totalValue h n p d b rho 0 0 0 0 0 = annMemberSpouse h n p d b rho := by sorry
Source
Originally derived two-life finite-grid definition or theorem, motivated by S. David Promislow (2015), Fundamentals of Actuarial Mathematics, third edition, Chapter 10, Section 10.6, p. 150. The published reference supplies actuarial context, while the formal statement and joint-law conventions are new. https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/
Human review

  • Endorsed by Shuze Chen · Oct 16, 2026

    Confirmed by the moderator at approval.

  • Endorsed by WillR · Oct 16, 2026

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

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