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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.08763 |
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| _version_ | 1866916994091057152 |
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| author | Laudagé, Christian Liebrich, Felix-Benedikt Sass, Jörn |
| author_facet | Laudagé, Christian Liebrich, Felix-Benedikt Sass, Jörn |
| contents | We revisit the recently introduced concept of return risk measures (RRMs) and extend it by incorporating risk management via multiple so-called eligible assets. The resulting new class of risk measures, termed multi-asset return risk measures (MARRMs), introduces a novel economic model for multiplicative risk sharing. We analyze properties of these risk measures. In particular, we prove that a positively homogeneous MARRM is quasi-convex if and only if it is convex. Furthermore, we provide conditions to avoid inconsistent risk evaluations. Then, we point out the connection between MARRMs and the well-known concept of multi-asset risk measures (MARMs). This is used to obtain various dual representations of MARRMs. Moreover, we conduct a series of case studies, in which we use typical continuous-time financial markets and different notions of acceptability of losses to compare RRMs, MARMs, and MARRMs and draw conclusions about the cost of risk mitigation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_08763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multi-asset return risk measures Laudagé, Christian Liebrich, Felix-Benedikt Sass, Jörn Mathematical Finance We revisit the recently introduced concept of return risk measures (RRMs) and extend it by incorporating risk management via multiple so-called eligible assets. The resulting new class of risk measures, termed multi-asset return risk measures (MARRMs), introduces a novel economic model for multiplicative risk sharing. We analyze properties of these risk measures. In particular, we prove that a positively homogeneous MARRM is quasi-convex if and only if it is convex. Furthermore, we provide conditions to avoid inconsistent risk evaluations. Then, we point out the connection between MARRMs and the well-known concept of multi-asset risk measures (MARMs). This is used to obtain various dual representations of MARRMs. Moreover, we conduct a series of case studies, in which we use typical continuous-time financial markets and different notions of acceptability of losses to compare RRMs, MARMs, and MARRMs and draw conclusions about the cost of risk mitigation. |
| title | Multi-asset return risk measures |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2411.08763 |