Prove2Me

Cause-contingent insurance and integral Thiele reserves: nhEndowment_no_payment

Proved
ActuarialValuation.nhEndowment_no_payment

by WillR · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

actuarial-scienceformal-verificationnonstationary-thiele-reserves

Zero terminal benefit has zero prospective endowment liability. This original derived actuarial relation uses the parameter restrictions, endpoints and units stated in the separate formal theorem or definition.

Mathematical relation:

V′(t)=(δ+λ(t))V(t)−λ(t)(pB1+(1−p)B2)V'(t)=(\delta+\lambda(t))V(t)-\lambda(t)\bigl(pB_1+(1-p)B_2\bigr)
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Analysis.SpecialFunctions.ExpDeriv
import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic
import Definitions.Def_actuarial_nhEndowment
Formal statement
namespace ActuarialValuation

theorem nhEndowment_no_payment (a b δ T t : ℝ) : nhEndowment a b δ T 0 t=0 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 30. S. David Promislow (2015), Fundamentals of Actuarial Mathematics, chapter 19, https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/ftoc.xhtml; Frederik Møller and colleagues, Multi-state modeling in the mathematics of life insurance, https://www.math.ku.dk/bibliotek/arkivet/phd-theses/phd20cf.pdf; Buchardt, Møller and Schmidt (2015), https://doi.org/10.1080/03461238.2013.879919. Parent topic: Nonstationary linear hazard, competing exits, absorbing three-state transition laws and differentiable integral prospective reserves. 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.math.ku.dk/bibliotek/arkivet/phd-theses/phd20cf.pdf
Human review

  • Endorsed by Shuze Chen · Oct 11, 2026

    Confirmed by the moderator at approval.

  • Endorsed by WillR · Oct 11, 2026

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

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