Multi-asset return risk measures

Christian Laudag\'e, Felix-Benedikt Liebrich and J\"orn Sass

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Abstract: 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.

Date: 2024-11, Revised 2025-04
New Economics Papers: this item is included in nep-rmg
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2411.08763

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