First and second finite difference smoothness: whSecondRoughness_nonneg
ProvedActuarialValuation.whSecondRoughness_nonnegactuarial-scienceformal-verificationmortality-graduation-smoothing
Finite squared second differences yield nonnegative curvature roughness. 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_whSecondRoughness
Formal statement
namespace ActuarialValuation theorem whSecondRoughness_nonneg (g : ℕ → ℝ) (n : ℕ) : 0 ≤ whSecondRoughness g n := by sorry end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 156. Casualty Actuarial Society (1968), Proceedings of the Casualty Actuarial Society Volume LV, Graduation section, https://www.casact.org/sites/default/files/database/proceed_proceed68_1968.pdf; Nels M. Valerius, Notes on Whittaker-Henderson Formula A, Proceedings of the Casualty Actuarial Society LIV (1967), p. 218, https://www.casact.org/sites/default/files/database/proceed_proceed67_67218.pdf. Parent topic: Actuarial graduation of crude mortality estimates, exposure-weighted data fidelity, first and second order finite difference roughness penalties. 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/proceed_proceed68_1968.pdf
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.