Fair estimation of capital risk allocation

Bielecki Tomasz R. (), Cialenco Igor (), Pitera Marcin () and Schmidt Thorsten ()
Additional contact information
Bielecki Tomasz R.: Department of Applied Mathematics, Illinois Institute of Technology, 10 W 32nd Str, Building REC, Room 220, Chicago, IL 60616, USA
Cialenco Igor: Department of Applied Mathematics, Illinois Institute of Technology, 10 W 32nd Str, Building REC, Room 220, Chicago, IL 60616, USA
Pitera Marcin: Institute of Mathematics, Jagiellonian University, Lojasiewicza 6, 30-348Cracow, Poland
Schmidt Thorsten: Department of Mathematical Stochastics, University of Freiburg, Eckerstr.1, 79104Freiburg, Germany

Statistics & Risk Modeling, 2020, vol. 37, issue 1-2, 1-24

Abstract: In this paper, we develop a novel methodology for estimation of risk capital allocation. The methodology is rooted in the theory of risk measures. We work within a general, but tractable class of law-invariant coherent risk measures, with a particular focus on expected shortfall. We introduce the concept of fair capital allocations and provide explicit formulae for fair capital allocations in case when the constituents of the risky portfolio are jointly normally distributed. The main focus of the paper is on the problem of approximating fair portfolio allocations in the case of not fully known law of the portfolio constituents. We define and study the concepts of fair allocation estimators and asymptotically fair allocation estimators. A substantial part of our study is devoted to the problem of estimating fair risk allocations for expected shortfall. We study this problem under normality as well as in a nonparametric setup. We derive several estimators, and prove their fairness and/or asymptotic fairness. Last, but not least, we propose two backtesting methodologies that are oriented at assessing the performance of the allocation estimation procedure. The paper closes with a substantial numerical study of the subject and an application to market data.

Keywords: Capital allocation; fair capital allocation; asymptotic fairness; expected shortfall; risk measures; Euler principle; value-at-risk; tail-value-at-risk; backtesting capital allocation (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1515/strm-2019-0011 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:strimo:v:37:y:2020:i:1-2:p:1-24:n:3

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/strm/html

DOI: 10.1515/strm-2019-0011

Access Statistics for this article

Statistics & Risk Modeling is currently edited by Robert Stelzer

More articles in Statistics & Risk Modeling from De Gruyter
Bibliographic data for series maintained by Peter Golla ().