Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.13539 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- In this paper, we investigate the robust models for $Λ$-quantiles with partial information regarding the loss distribution, where $Λ$-quantiles extend the classical quantiles by replacing the fixed probability level with a probability/loss function $Λ$. We find that, under some assumptions, the robust $Λ$-quantiles equal the $Λ$-quantiles of the extremal distributions. This finding allows us to obtain the robust $Λ$-quantiles by applying the results of robust quantiles in the literature. Our results are applied to uncertainty sets characterized by three different constraints respectively: moment constraints, probability distance constraints via the Wasserstein metric, and marginal constraints in risk aggregation. We obtain some explicit expressions for robust $Λ$-quantiles by deriving the extremal distributions for each uncertainty set. These results are applied to optimal portfolio selection under model uncertainty.