Estimating the VaR-induced Euler allocation rule

• DOI: 10.1017/asb.2023.17
• Publication Date: 2023-05-02T10:54:11Z
• Authors: N.V. Gribkova; J. Su; R. Zitikis
• Keywords: Conditional expectation; Statistical Inference; Quantile; Quantile regression

Abstract The prominence of the Euler allocation rule (EAR) is rooted in fact that it only return on risk-adjusted capital (RORAC) compatible rule. When total regulatory set using value-at-risk (VaR), EAR becomes – a statistical term quantile-regression (QR) function. Although cumulative QR function (i.e., an integral function) has received considerable attention literature, fully developed inference theory for itself been elusive. In present paper, we develop such based empirical estimator, which establish consistency, asymptotic normality, and standard error estimation. This makes herein results readily applicable practice, thus facilitating decision making within RORAC paradigm, conditional mean risk sharing, current frameworks.