Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.13138 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915409770315776 |
|---|---|
| author | Chambers, Christopher Miller, Alan Wang, Ruodu Wu, Qinyu |
| author_facet | Chambers, Christopher Miller, Alan Wang, Ruodu Wu, Qinyu |
| contents | Max-stability is the property that taking a maximum between two inputs results in a maximum between two outputs. We study max-stability with respect to first-order stochastic dominance, the most fundamental notion of stochastic dominance in decision theory. Under two additional standard axioms of nondegeneracy and lower semicontinuity, we establish a representation theorem for functionals satisfying max-stability, which turns out to be represented by the supremum of a bivariate function. A parallel characterization result for min-stability, that is, with the maximum replaced by the minimum in max-stability, is also established. By combining both max-stability and min-stability, we obtain a new characterization for a class of functionals, called the Lambda-quantiles, that appear in finance and political science. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Max- and min-stability under first-order stochastic dominance Chambers, Christopher Miller, Alan Wang, Ruodu Wu, Qinyu Mathematical Finance Probability Max-stability is the property that taking a maximum between two inputs results in a maximum between two outputs. We study max-stability with respect to first-order stochastic dominance, the most fundamental notion of stochastic dominance in decision theory. Under two additional standard axioms of nondegeneracy and lower semicontinuity, we establish a representation theorem for functionals satisfying max-stability, which turns out to be represented by the supremum of a bivariate function. A parallel characterization result for min-stability, that is, with the maximum replaced by the minimum in max-stability, is also established. By combining both max-stability and min-stability, we obtain a new characterization for a class of functionals, called the Lambda-quantiles, that appear in finance and political science. |
| title | Max- and min-stability under first-order stochastic dominance |
| topic | Mathematical Finance Probability |
| url | https://arxiv.org/abs/2403.13138 |