Monetary Risk Measures [article]

Guangyan Jia, Jianming Xia, Rongjie Zhao
2020 arXiv   pre-print
In this paper, we study general monetary risk measures (without any convexity or weak convexity). A monetary (respectively, positively homogeneous) risk measure can be characterized as the lower envelope of a family of convex (respectively, coherent) risk measures. The proof does not depend on but easily leads to the classical representation theorems for convex and coherent risk measures. When the law-invariance and the SSD (second-order stochastic dominance)-consistency are involved, it is not
more » ... the convexity (respectively, coherence) but the comonotonic convexity (respectively, comonotonic coherence) of risk measures that can be used for such kind of lower envelope characterizations in a unified form. The representation of a law-invariant risk measure in terms of VaR is provided.
arXiv:2012.06751v1 fatcat:ygk3lyjyqzckhdkv4ubnlzotiq