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VECTOR-VALUED COHERENT RISK MEASURE PROCESSES

Emmanuel Lépinette, Imen Ben Tahar

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Abstract

Introduced by Artzner et al. (1998) the axiomatic characterization of a static coherent risk measure was extended by Jouini et al. (2004) in a multi-dimensional setting to the concept of vector-valued risk measures. In this paper, we propose a dynamic version of the vector-valued risk measures in a continuous-time framework. Particular attention is devoted to the choice of a convenient risk space. We provide dual characterization results, we study different notions of time consistency and we give examples of vector-valued risk measure processes.

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What this paper is about

Introduced by Artzner et al. (1998) the axiomatic characterization of a static coherent risk measure was extended by Jouini et al. (2004) in a multi-dimensional setting to the concept of vector-valued risk measures. In this paper, we propose a dynamic version of the vector-valued risk measures in a continuous-time framework. Particular attention is devoted to the choice of a convenient risk space. We provide dual characterization results, we study different notions of time consistency and we give examples of vector-valued risk measure processes.

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Available abstract

Introduced by Artzner et al. (1998) the axiomatic characterization of a static coherent risk measure was extended by Jouini et al. (2004) in a multi-dimensional setting to the concept of vector-valued risk measures. In this paper, we propose a dynamic version of the vector-valued risk measures in a continuous-time framework. Particular attention is devoted to the choice of a convenient risk space. We provide dual characterization results, we study different notions of time consistency and we give examples of vector-valued risk measure processes.

Key concepts: Dynamic risk measure, Measure (data warehouse), Time consistency, Coherent risk measure, Risk measure, Characterization (materials science), Axiom, Dual (grammatical number)

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