Bootstrapping Average Value at Risk of Single and Collective Risks

Abstract

Almost sure bootstrap consistency of the blockwise bootstrap for the Average Value at Risk of single risks is established for strictly stationary β -mixing observations. Moreover, almost sure bootstrap consistency of a multiplier bootstrap for the Average Value at Risk of collective risks is established for independent observations. The main results rely on a new functional delta-method for the almost sure bootstrap of uniformly quasi-Hadamard differentiable statistical functionals, to be presented here. The latter seems to be interesting in its own right.

Keywords

• Average Value at Risk
• compound distribution
• nonparametric estimation
• multiplier bootstrap
• blockwise bootstrap
• functional delta-method
• uniform quasi-Hadamard differentiability
• chain rule