Prove2Me

Deterministic zero-coupon bonds and forward discounts: bdAnnualForward_one

Proved
ActuarialValuation.bdAnnualForward_one

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

actuarial-sciencediscount-curves-bond-pricingformal-verification

One-year forward rate equals gross single-period forward return minus one.

Mathematical relation:

bdAnnualForward_onebdAnnualForward\_one

Original derived theorem target; the Lean statement gives the exact conditions and result.

Preamble
import Mathlib.Data.Real.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Analysis.SpecialFunctions.Exp
import Definitions.Def_actuarial_bdAnnualForward
import Definitions.Def_actuarial_bdForwardGross
Formal statement
namespace ActuarialValuation

theorem bdAnnualForward_one (D : ℕ → ℝ) (t : ℕ) : bdAnnualForward D t = bdForwardGross D t (t+1)-1 := by sorry

end ActuarialValuation
Source
Original derived actuarial mathematics inspired by Promislow (2015), chapters 2.12–2.13 and 20.13, published book reference https://www.oreilly.com/library/view/fundamentals-of-actuarial/9781118782521/; supporting published actuarial reference https://www.jstor.org/stable/2951677. The proposed model is rooted in Promislow chapter 2.12–2.13 and 20.13. The target Lean identity is an original derivation, not a verbatim published result. Published source page 367 gives the thematic chapter context, rather than an exact statement of this new formal theorem.
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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