Bootstrapping Average Value at Risk of Single and Collective Risks

• Main Authors: Eric Beutner, Henryk Zähle
• Format: Article
• Language: English
• Published: MDPI AG 2018-09-01
• Series: Risks
• Subjects: Average Value at Risk; compound distribution; nonparametric estimation; multiplier bootstrap; blockwise bootstrap; functional delta-method; uniform quasi-Hadamard differentiability; chain rule
• Online Access: http://www.mdpi.com/2227-9091/6/3/96

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.