TY - JOUR

T1 - Estimating the VaR-induced Euler allocation rule

AU - Gribkova, N.V.

AU - Su, Jianxi

AU - Zitikis, Ricardas

N1 - N.V. Gribkova, J. Su, and R. Zitikis, Estimating the VaR-induced Euler allocation rule, ASTIN Bulletin: The Journal of the IAA , First View , pp. 1 - 17 (Published online by Cambridge University Press: 02 May 2023), DOI: https://doi.org/10.1017/asb.2023.17

PY - 2023/9/2

Y1 - 2023/9/2

N2 - The prominence of the Euler allocation rule (EAR) is rooted in the fact that it is the only return on risk-adjusted capital (RORAC) compatible capital allocation rule. When the total regulatory capital is set using the value-at-risk (VaR), the EAR becomes – using a statistical term – the quantile-regression (QR) function. Although the cumulative QR function (i.e., an integral of the QR function) has received considerable attention in the literature, a fully developed statistical inference theory for the QR function itself has been elusive. In the present paper, we develop such a theory based on an empirical QR estimator, for which we establish consistency, asymptotic normality, and standard error estimation. This makes the herein developed results readily applicable in practice, thus facilitating decision making within the RORAC paradigm, conditional mean risk sharing, and current regulatory frameworks.

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

KW - Capital allocations

KW - conditional mean risk sharing

KW - Quantile regression

KW - order statistics

KW - concomitants

KW - Capital allocations

KW - conditional mean risk sharing

KW - quantile regression

KW - order statistics

KW - concomitants

UR - https://www.mendeley.com/catalogue/e2f56655-4840-3af3-ba60-4b9c719c33b3/

U2 - 10.1017/asb.2023.17

DO - 10.1017/asb.2023.17

M3 - Article

VL - 53

SP - 619

EP - 635

JO - ASTIN Bulletin

JF - ASTIN Bulletin

SN - 0515-0361

IS - 3

ER -