Age-period Lee-Carter log mortality and drift: lcDriftIndex_zero
ProvedActuarialValuation.lcDriftIndex_zeroactuarial-scienceformal-verificationlee-carter-mortality
No projection time means unchanged mortality index. 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 Mathlib.Analysis.SpecialFunctions.ExpDeriv import Definitions.Def_actuarial_lcDriftIndex
Formal statement
namespace ActuarialValuation theorem lcDriftIndex_zero (initial drift : ℝ) : lcDriftIndex initial drift 0 = initial := by sorry end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 659. Ronald D. Lee and Lawrence R. Carter, Modeling and Forecasting U.S. Mortality, Journal of the American Statistical Association 87 (1992), pp. 659–671, https://doi.org/10.1080/01621459.1992.10475265; U.S. Social Security Administration, Out-of-Sample Performance of Stochastic Methods in Forecasting Age-Specific Mortality Rates (2008), https://www.ssa.gov/policy/docs/workingpapers/wp111.html. Parent topic: Age-period Lee-Carter mortality surface, log-linear mortality rate ratios, finite deterministic projection and cohort survival valuation. 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://doi.org/10.1080/01621459.1992.10475265
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.