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Southwest Jiaotong University School of Mathematics

# Robust representations of risk measures on Orlicz spaces

Robust representations of risk measures on Orlicz spaces

Niushan Gao

Department of Mathematics

Ryerson University

In this talk, we will review the theoretical framework for quantifying market risk of financial institutions in terms of coherent risk measures, which was laid in a seminal paper of Artzner et al.~(1999). For a coherent risk measure on L^\infty, Delbaen (2002) proved that $\rho$ can be represented as the worst expectation over a class of probabilities whenever it has the Fatou property. Lately, it has been asked whether Delbaen's representation theorem holds on more general model spaces containing unbounded positions. We will present a comprehensive investigation on this problem. We characterize the Orlicz spaces over which the representation holds. We also show that the representation holds on general Orlicz spaces if the risk measure possess additional properties, e.g., law-invariance or surplus-invariance.