Prove2Me

Equivalence premiums and loss variance: pvExpected_zero

Proved
ActuarialValuation.pvExpected_zero

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

actuarial-scienceformal-verificationinsurance-loss-distributions

Any finite loss distribution has zero expected value for a zero random loss.

Mathematical relation:

pvExpected_zeropvExpected\_zero

Original derived theorem target; the Lean statement gives the exact conditions and result.

Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_pvExpected
Formal statement
namespace ActuarialValuation

theorem pvExpected_zero {n : ℕ} (p : Fin n → ℝ) : pvExpected p (fun _ => 0) = 0 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics inspired by Promislow (2015), chapters 15 and 16, published book reference https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/; supporting published actuarial reference https://www.soa.org/globalassets/assets/files/edu/fall2006webcatalog.pdf. Published source page 235 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

  • 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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