Kavli Affiliate: Ran Wang
| First 5 Authors: Xiangyu Han, Xiangyu Han, , ,
| Summary:
In this paper, by proposing two new kinds of distributional uncertainty sets,
we explore robustness of distortion risk measures against distributional
uncertainty. To be precise, we first consider a distributional uncertainty set
which is characterized solely by a ball determined by general Wasserstein
distance centered at certain empirical distribution function, and then further
consider additional constraints of known first moment and any other higher
moment of the underlying loss distribution function. Under the assumption that
the distortion function is strictly concave and twice differentiable, and that
the underlying loss random variable is non-negative and bounded, we derive
closed-form expressions for the distribution functions which maximize a given
distortion risk measure over the distributional uncertainty sets respectively.
Moreover, we continue to study the general case of a concave distortion
function and unbounded loss random variables. Comparisons with existing studies
are also made. Finally, we provide a numerical study to illustrate the proposed
models and results. Our work provides a novel generalization of several known
achievements in the literature.
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