Regular contributions and fund first/second-moment recursions: siFundSecondNext_zero_contribution

Proved

ActuarialValuation.siFundSecondNext_zero_contribution

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

actuarial-scienceformal-verificationstochastic-investment-accumulation

Second moment without contributions compounds using the second gross moment. This original derived actuarial relation uses the parameter restrictions, endpoints and units stated in the separate formal theorem or definition.

Mathematical relation:

A_{n+1}=(A_n+c)G_{n+1},\quad m_{n+1}=(m_n+c)\bar G

Preamble

import Mathlib.Data.Real.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Definitions.Def_actuarial_siFundSecondNext

Formal statement

namespace ActuarialValuation

theorem siFundSecondNext_zero_contribution (priorSecond priorMean secondGross : ℝ) : siFundSecondNext priorSecond priorMean 0 secondGross=priorSecond*secondGross := by sorry

end ActuarialValuation

Source

Original derived actuarial mathematics, published source page 13. S. David Promislow, Fundamentals of Actuarial Mathematics (2015), Chapters on stochastic rates and annuity accumulation; Shreve (2004), Stochastic Calculus for Finance I, Chapter 1, https://link.springer.com/book/10.1007/978-0-387-22527-2. Parent topic: Finite-scenario expectation and variance; fixed random rate versus independent annual rates, product sample space and fund contribution moments. 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://link.springer.com/book/10.1007/978-0-387-22527-2

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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