Prove2Me

Compound Poisson Panjer recurrence: panjerPoissonZero_zero

Proved
ActuarialValuation.panjerPoissonZero_zero

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

actuarial-sciencecompound-claims-panjerformal-verification

Zero annual claim intensity produces certain zero aggregate loss. 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:

e0=1e^0=1
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Analysis.SpecialFunctions.ExpDeriv
import Definitions.Def_actuarial_panjerPoissonZero
Formal statement
namespace ActuarialValuation

theorem panjerPoissonZero_zero  : panjerPoissonZero 0 = 1 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 22. Harry H. Panjer, Recursive Evaluation of a Family of Compound Distributions, ASTIN Bulletin 12 (1981), pp. 22-26, https://www.casact.org/sites/default/files/database/astin_vol12no1_22.pdf; Sundt and Jewell, Further Results on Recursive Evaluation of Compound Distributions, ASTIN Bulletin 12 (1981), https://www.casact.org/sites/default/files/database/astin_vol12no1_27.pdf. Parent topic: Finite lattice claim severities, compound Poisson aggregate claim coefficients and Panjer recurrence with strictly positive claim sizes. 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.casact.org/sites/default/files/database/astin_vol12no1_22.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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