Prove2Me

Stopped exponential-loss process and conditional Lundberg capital bound: srBound_at_zero

Proved
ActuarialValuation.srBound_at_zero

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

actuarial-scienceformal-verificationstochastic-ruin-firstpassage

With no starting capital the upper bound is one. This original derived actuarial relation uses the parameter restrictions, endpoints and units stated in the separate formal theorem or definition.

Mathematical relation:

E[Mτ∧N]≤1 ⟹ ψN(u)≤e−Ru\mathbb{E}[M_{\tau\wedge N}]\le1\ \Longrightarrow\ \psi_N(u)\le e^{-Ru}
Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
import Mathlib.MeasureTheory.Integral.Bochner.Basic
import Mathlib.Analysis.SpecialFunctions.ExpDeriv
import Definitions.Def_actuarial_srLundbergBound
Formal statement
namespace ActuarialValuation

theorem srBound_at_zero (R : ℝ) : srLundbergBound R 0=1 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 3. S. David Promislow (2015), Fundamentals of Actuarial Mathematics, chapter 23, https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/ftoc.xhtml; Hanspeter Schmidli, Risk Theory (2017), https://link.springer.com/book/10.1007/978-3-319-72005-0; probability ruin bound overview https://www.mdpi.com/2227-9091/12/2/28. Parent topic: Actual compound-Poisson embedded arrival paths, measurable first ruin events, disjoint first-hit times, deficit and conditional stopped-exponential Lundberg bound. 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.mdpi.com/2227-9091/12/2/28
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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