University of Vienna
Law invariant risk measures on L∞(Rd)
Kusuoka (2001) has obtained explicit representation theorems for
comonotone risk measures and, more generally, for law invariant risk
measures. These theorems pertain, like most of the previous literature,
to the case of scalar-valued risks.
Jouini-Meddeb-Touzi (2004) and Burgert-Ruschendorf (2006) extended
the notion of risk measures to the vector-valued case. Recently
Ekeland-Galichon-Henry (2009) obtained extensions of the above theorems
of Kusuoka to this setting. Their results were conned to the
In general, Kusuoka's representation theorem for comonotone risk
measures also involves a singular part. In the present work we give
a full generalization of Kusuoka's theorems to the vector-valued case.
The singular component turns out to have a richer structure than in
the scalar case.
Joint work with Ivar Ekeland.