Composite graduation objective and invariance: whObjectiveOne_zero_smooth
ProvedActuarialValuation.whObjectiveOne_zero_smoothactuarial-scienceformal-verificationmortality-graduation-smoothing
A perfectly smooth curve has only the data-fidelity component. 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_whObjectiveOne
Formal statement
namespace ActuarialValuation theorem whObjectiveOne_zero_smooth (fit lambda : ℝ) : whObjectiveOne fit 0 lambda = fit := 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.