Prove2Me

Two-module capital charges and correlation cross terms: scrPairSquared_unit

Proved
ActuarialValuation.scrPairSquared_unit

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

actuarial-scienceformal-verificationsolvency-correlation-capital

Perfect positive correlation gives squared capital sum. 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:

Q1=(C1+C2)2Q_1=(C_1+C_2)^2
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_scrPairSquared
import Definitions.Def_actuarial_scrSumSquared
Formal statement
namespace ActuarialValuation

theorem scrPairSquared_unit (a b : ℝ) : scrPairSquared 1 a b = scrSumSquared a b := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 3. European Union (2009), Solvency II Directive 2009/138/EC, Article 104 and Annex IV, https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32009L0138; Bank of England Prudential Regulation Authority (2024), Standard Formula Annexes, https://www.bankofengland.co.uk/-/media/boe/files/prudential-regulation/policy-statement/2024/november/ps1524app7.pdf. Parent topic: Correlation-based insurance capital aggregation, systematic cross terms, quadratic risk charges and diversification benefits. 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.bankofengland.co.uk/-/media/boe/files/prudential-regulation/policy-statement/2024/november/ps1524app7.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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