Discrete cumulative tails, thresholds and monetary shifts: tailCDF_zero_range
ProvedActuarialValuation.tailCDF_zero_rangeactuarial-scienceformal-verificationtail-risk-cvar
Loss zero is never excluded by a nonnegative threshold. 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_tailCDF
Formal statement
namespace ActuarialValuation theorem tailCDF_zero_range (p : ℕ → ℝ) (t : ℕ) : tailCDF p 0 t = p 0 := by sorry end ActuarialValuation
Source
Original derived actuarial mathematics, published source page 5. Rockafellar and Uryasev, Optimization of Conditional Value-at-Risk (1999 preprint, later Journal of Risk 2000), equation 4 and Theorem 1, page 5, https://sites.math.washington.edu/~rtr/papers/rtr179-CVaR1.pdf; Rockafellar and Uryasev, Journal of Risk (2000), https://econpapers.repec.org/RePEc:rsk:journ4:2161159. Parent topic: Finite discrete loss distributions, excess-of-loss functionals and Rockafellar-Uryasev conditional value-at-risk auxiliary threshold objective. 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://sites.math.washington.edu/~rtr/papers/rtr179-CVaR1.pdf
Human review
Confirmed by the mission captain (proposal self-audit).
Confirmed by the moderator at approval.