Asymptotic properties of conditional value-at-risk estimate for asymptotic negatively associated samples

Abstract

Abstract This article examines the strong consistency of the conditional value-at-risk (CVaR) estimate for asymptotic negatively associated (ANA or ρ − $\rho ^{-}$ , for short) random samples under mild conditions. It is demonstrated that the optimal rate can achieve nearly O ( n − 1 / 2 ) $O (n^{-1/2})$ under certain appropriate conditions. Furthermore, we present numerical simulations and a real data example to corroborate our theoretical results based on finite samples.

Keywords

• Asymptotic negatively associated random variables
• Conditional value-at-risk estimate
• Strong consistency
• Auto-regressive moving average model
• Stock data