Inference for the Euler allocation rules induced by the Tail Conditional Expectation and Value-at-Risk

Inference for the Euler Allocation Rules Induced by the Tail Conditional Expectation and Value-at-Risk

Fall 2022 Actuarial Science and Financial Mathematics Seminar

Date and Time: Friday, October 28, 2022, 2:00 PM (CST)

Speaker: Jianxi Su (Purdue University)

Abstract: 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) and the Tail Conditional Expectation (TCE), the EAR becomes—using a statistical term—the quantile-regression function and its cumulative variant, respectively.  In the present talk, we develop a statistical inference theory for the VaR-induced and TCE-induced EAR’s based on empirical estimators, 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.

About: Jianxi Su is an Associate Professor of Actuarial Science at Purdue University. His research expertise ranges from mathematics/statistics modeling to diverse applications in insurance. He has published in such reputable actuarial journals as ASTIN Bulletin, Insurance: Mathematics and Economics, Journal of Risk and Insurance. Over the past several years, he has successfully completed numerous research projects sponsored by the SOA and CAS. He has ample industrial experience with the ORSA team of Sun Life Financial, Canada.