Prove2Me

Risk guarantees, surrender payments and reserve strain: ulNetAmountAtRisk_zero

Proved
ActuarialValuation.ulNetAmountAtRisk_zero

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

actuarial-scienceformal-verificationunit-linked-profit-charges

A fund above its guaranteed benefit needs no extra mortality risk cover. This original derived actuarial relation uses the parameter restrictions, endpoints and units stated in the separate formal theorem or definition.

Mathematical relation:

Btdeath=max⁡(Ft,Gt),Rt=(Gt−Ft)+B_t^{\text{death}}=\max(F_t,G_t),\quad R_t=(G_t-F_t)^+
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.Order.Group.MinMax
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_ulNetAmountAtRisk
Formal statement
namespace ActuarialValuation

theorem ulNetAmountAtRisk_zero (fund guarantee : ℝ) (h : guarantee≤fund) : ulNetAmountAtRisk fund guarantee=0 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 16. FCA, Unit-linked pensions and savings price and value practices, https://www.fca.org.uk/publications/multi-firm-reviews/unit-linked-pensions-and-savings-multi-firm-review-consumer-duty-price-and-value-practices; FCA TR16/2 Fair treatment of long-standing customers, https://www.fca.org.uk/your-fca/documents/thematic-reviews/tr16-02. Parent topic: Allocated premium, offer and bid unit prices, cost of allocation spread, fund charges, net amount at risk, policy expenses and discounted expected non-unit profit. 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.fca.org.uk/your-fca/documents/thematic-reviews/tr16-02
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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