Fractional premiums and policy reserves: frReserve_zero_mortality
ProvedActuarialValuation.frReserve_zero_mortalityactuarial-scienceformal-verificationfractional-life-valuation
When annual mortality is zero, conditional reserve reduces to accumulated opening assets and premium.
Mathematical relation:
Original derived theorem target; the Lean statement gives the exact conditions and result.
Preamble
import Mathlib.Data.Real.Basic import Mathlib.Algebra.BigOperators.Group.Finset.Basic import Mathlib.Analysis.SpecialFunctions.Exp import Definitions.Def_actuarial_frFractionalReserve
Formal statement
namespace ActuarialValuation theorem frReserve_zero_mortality (assets premium benefit s growth endDiscount : ℝ) : frFractionalReserve assets premium benefit 0 s growth endDiscount = (assets+premium)*growth := by sorry end ActuarialValuation
Source
Original derived actuarial mathematics inspired by Promislow (2015), chapters 7, 4 and 8, published book reference https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/; supporting published actuarial reference https://www.soa.org/498941/globalassets/assets/files/e-business/pd/events/2018/las/pd-2018-05-las-session-033.pdf. Published source page 98 of Promislow's 2015 edition provides the thematic mathematical context. The target Lean identity is an original derivation, not a verbatim published result.
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.