Vector-valued coherent risk measures

Elyès Jouini; Moncef Meddeb; Nizar Touzi

doi:10.1007/s00780-004-0127-6

Vector-valued coherent risk measures

Elyès Jouini, Moncef Meddeb, Nizar Touzi

Finance and Risk Engineering

Research output: Contribution to journal › Review article › peer-review

Abstract

We define (d, n)-coherent risk measures as set-valued maps from L _d ^∞ into ℝ ⁿ satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the passage from ℝ ^d-valued random portfolio to ℝ ⁿ-valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided.

Original language	English (US)
Pages (from-to)	531-552
Number of pages	22
Journal	Finance and Stochastics
Volume	8
Issue number	4
DOIs	https://doi.org/10.1007/s00780-004-0127-6
State	Published - Nov 2004

Keywords

Coherent risk measures
Liquidity risk
Risk aggregation

ASJC Scopus subject areas

Statistics and Probability
Finance
Statistics, Probability and Uncertainty

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10.1007/s00780-004-0127-6

Cite this

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abstract = "We define (d, n)-coherent risk measures as set-valued maps from L d ∞ into ℝ n satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the passage from ℝ d-valued random portfolio to ℝ n-valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided.",

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AU - Meddeb, Moncef

AU - Touzi, Nizar

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AB - We define (d, n)-coherent risk measures as set-valued maps from L d ∞ into ℝ n satisfying some axioms. We show that this definition is a convenient extension of the real-valued risk measures introduced by Artzner et al. [2]. We then discuss the aggregation issue, i.e., the passage from ℝ d-valued random portfolio to ℝ n-valued measure of risk. Necessary and sufficient conditions of coherent aggregation are provided.

KW - Coherent risk measures

KW - Liquidity risk

KW - Risk aggregation

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JO - Finance and Stochastics

JF - Finance and Stochastics

IS - 4

ER -

Vector-valued coherent risk measures

Abstract

Keywords

ASJC Scopus subject areas

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