Text

A Theory for Measures of Tail Risk

The notion of “tail risk” has been a crucial consideration in modern risk management and financial regulation, as very well documented in the recent regulatory documents. To achieve a comprehensive understanding of the tail risk, we carry out an axiomatic study for risk measures that quantify the tail risk, that is, the behaviour of a risk beyond a certain quantile. Such risk measures are referred to as tail risk measures in this paper. The two popular classes of regulatory risk measures in banking and insurance, value at risk (VaR) and expected shortfall, are prominent, yet elementary, examples of tail risk measures. We establish a connection between a tail risk measure and a corresponding law-invariant risk measure, called its generator, and investigate their joint properties. A tail risk measure inherits many properties from its generator, but not subadditivity or convexity; nevertheless, a tail risk measure is coherent if and only if its generator is coherent. We explore further relevant issues on tail risk measures, such as bounds, distortion risk measures, risk aggregation, elicitability, and dual representations. In particular, there is no elicitable tail convex risk measure other than the essential supremum, and under a continuity condition, the only elicitable and positively homogeneous monetary tail risk measures are the VaRs.

Ketersediaan

Informasi Detail

Judul Seri

MATHEMATICS OF OPERATIONS RESEARCH; Vol.46 No.3 August 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1109 - 1128

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

VALUE AT RISK
BASEL III
RISK AGGREGATION
ELICITABILITY
TAIL RISK

Info Detail Spesifik

https://doi.org/10.1287/moor.2020.1072

Pernyataan Tanggungjawab

Fangda Liu, Ruodu Wang

Versi lain/terkait

Lampiran Berkas

Komentar