Premium and claim surplus cash-flow recursion: ruClaimTotal_nonneg
ProvedActuarialValuation.ruClaimTotal_nonnegactuarial-scienceformal-verificationruin-deficit-process
Nonnegative claims yield nonnegative aggregate payments. 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_ruClaimTotal
Formal statement
namespace ActuarialValuation theorem ruClaimTotal_nonneg (x : ℕ → ℝ) (n : ℕ) (hx : ∀ k ∈ Finset.range n, 0 ≤ x k) : 0 ≤ ruClaimTotal x n := by sorry end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 433. S. David Promislow, Fundamentals of Actuarial Mathematics, third edition (2015), Chapter 23, https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/ftoc.xhtml; Palmowski, Ramsden and Papaioannou (2018), Parisian ruin for the dual risk process in discrete-time, https://link.springer.com/article/10.1007/s13385-018-0172-8. Parent topic: Actuarial surplus and ruin: first-passage event, claim timing, nonnegative deficit, retained loss and reinsurance comparison for finite portfolios. 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.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/ftoc.xhtml
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.