Worst-case distortion risk measures of transformed losses with uncertain distributions lying in Wasserstein balls

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      <subfield code="a">Worst-case distortion risk measures of transformed losses with uncertain distributions lying in Wasserstein balls</subfield>
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      <subfield code="a">This paper studies the worst-case distortion risk measures of the limited stop-loss transformtogether with its special cases, the stop-loss and limited loss transformswhen the underlying loss distribution is uncertain and lies within a general kkk-order Wasserstein ball around a reference distribution. We derive explicit expressions for these worst-case risk measures and identify the corresponding worst-case distributions. Our results also recover the findings of Guan et al. (2023) on worst-case stop-loss premiums under Wasserstein uncertainty. Numerical examples illustrate the worst-case distributions and risk measures, and we examine how the reference distribution, the Wasserstein ball radius, and the retention levels affect premiums for limited stop-loss reinsurance</subfield>
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