Finite count, severity and convolution transforms: cxPairTransform_unit
ProvedActuarialValuation.cxPairTransform_unitactuarial-sciencecompound-risk-transformsformal-verification
The independent joint probability law normalises when each marginal mass normalises. 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_cxPairTransform import Definitions.Def_actuarial_cxMass
Formal statement
namespace ActuarialValuation theorem cxPairTransform_unit (f g : ℕ → ℝ) (n m : ℕ) : cxPairTransform f g n m 1 = cxMass f n * cxMass g m := by sorry end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 393. S. David Promislow, Fundamentals of Actuarial Mathematics, third edition (2015), Chapter 21, https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/ftoc.xhtml; H. H. Panjer, Recursive Evaluation of a Family of Compound Distributions (1981), https://doi.org/10.1017/S0515036100006796. Parent topic: Compound aggregate risk: convolution and probability generating functions, zero claim severity mass, first two moments and (a,b,0) Panjer recurrence. 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.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/ftoc.xhtml
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.