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 webinar, we will 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.

Jianxi Su, PhD, FSA, is an Associate Professor in the Department of Statistics at Purdue University, where he also serves as the Director of the Actuarial Science Program. His research expertise ranges from mathematics/statistics modeling to diverse applications in insurance. Over the past several years, he has successfully completed numerous research projects sponsored by the SOA and CAS.  

Lukasz Delong is working at SGH Warsaw School of Economics. He has a PhD in mathematics, a habilitation degree in economics and the professor title in economics and finance. Lukasz is an actuary with license no. 130 issued by the Polish Financial Supervision Authority, the head of the Examination Committee for Actuaries at the Polish Financial Supervision Authority, a board member of the Polish Society of Actuaries and a board member of AFIR-ERM Section of the IAA. He is an editor of ASTIN Bulletin - The Journal of the IAA and an associate editor of European Actuarial Journal. Lukasz is an author of numerous scientific papers on insurance mathematics, financial mathematics and probability. His scientific research includes different areas of actuarial mathematics with emphasis on stochastic modelling of financial risks and machine learning in insurance.