Prove2Me

Finite-state transition and probability conservation: msRowMass_zero

Proved
ActuarialValuation.msRowMass_zero

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

actuarial-scienceformal-verificationmulti-state-reserves

An empty outgoing transition law has zero rather than unit row mass. 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:

Σj0=0Σ_j0=0
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Definitions.Def_actuarial_msRowMass
Formal statement
namespace ActuarialValuation

theorem msRowMass_zero (T : Fin 3 → Fin 3 → ℝ) (i : Fin 3) (h : ∀ j, T i j=0) : msRowMass T i = 0 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 305. S. David Promislow, Fundamentals of Actuarial Mathematics, third edition (2015), Chapter 19, https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/ftoc.xhtml; Dickson Hardy Waters (2009), Actuarial Mathematics for Life Contingent Risks, Chapter 8, https://www.cambridge.org/core/books/abs/actuarial-mathematics-for-life-contingent-risks/multiple-state-models/BFEB2CD04A3EA012FCB1C7E3A326E9A0; Buchardt, Møller and Schmidt, Cash flows and policyholder behaviour in the semi-Markov life insurance setup (2015), https://www.tandfonline.com/doi/full/10.1080/03461238.2013.879919. Parent topic: Finite discrete-time nonstationary and duration-dependent multi-state actuarial benefits, transition probabilities, reserve recursion, disability and surrender cashflows. 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.cambridge.org/core/books/abs/actuarial-mathematics-for-life-contingent-risks/multiple-state-models/BFEB2CD04A3EA012FCB1C7E3A326E9A0
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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