Prove2Me

Mortality rate ratios and force-to-probability conversion: lcDeathProb_lt_one

Proved
ActuarialValuation.lcDeathProb_lt_one

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

actuarial-scienceformal-verificationlee-carter-mortality

Finite force implies death probability strictly below one. 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:

q<1q<1
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Analysis.SpecialFunctions.ExpDeriv
import Definitions.Def_actuarial_lcDeathProb
Formal statement
namespace ActuarialValuation

theorem lcDeathProb_lt_one (force : ℝ) : lcDeathProb force < 1 := 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

  • 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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