Prove2Me

Cause-contingent insurance and integral Thiele reserves: nhCauseBenefit_at_zero

Proved
ActuarialValuation.nhCauseBenefit_at_zero

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

actuarial-scienceformal-verificationnonstationary-thiele-reserves

All exits receive the second contractual benefit at cause share zero. 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_nhCauseBenefit
Formal statement
namespace ActuarialValuation

theorem nhCauseBenefit_at_zero (B1 B2 : ℝ) : nhCauseBenefit 0 B1 B2=B2 := 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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