Paid-up insurance and equivalent cover: alterationPaidUpValue_zero
ProvedActuarialValuation.alterationPaidUpValue_zeroactuarial-scienceformal-verificationpolicy-reserve-alterations
A paid-up policy with zero benefit has zero reserve capital value. The full Lean declaration specifies the finite boundaries, exact units and any positivity, independence or regularity assumptions. This is an original derived Actuarial mathematical statement, not a claim of a numbered previously published theorem.
Mathematical relation:
Preamble
import Mathlib.Data.Real.Basic import Mathlib.Algebra.BigOperators.Group.Finset.Basic import Definitions.Def_actuarial_alterationPaidUpValue
Formal statement
namespace ActuarialValuation theorem alterationPaidUpValue_zero (A : ℝ) : alterationPaidUpValue 0 A = 0 := by sorry end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 90. S. David Promislow, Fundamentals of Actuarial Mathematics (2010/2015), Chapter 6, Section 6.8, Premium difference and paid-up formulas, https://onlinelibrary.wiley.com/doi/10.1002/9781119971528.ch6; Dickson Hardy Waters (2009), Actuarial Mathematics for Life Contingent Risks, policy values, https://www.cambridge.org/core/books/actuarial-mathematics-for-life-contingent-risks/51C0B04099D4DE1D1DDEF9551024133B/listing. Parent topic: Prospective life insurance policy reserves, premium differences, paid-up insurance amounts and surrender values. 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://onlinelibrary.wiley.com/doi/10.1002/9781119971528.ch6
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.