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Dynamic star-shaped risk measures and $g$-expectations

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  • Dejian Tian
  • Xunlian Wang

Abstract

Motivated by the results of static monetary or star-shaped risk measures, the paper investigates the representation theorems in the dynamic framework. We show that dynamic monetary risk measures can be represented as the lower envelope of a family of dynamic convex risk measures, and normalized dynamic star-shaped risk measures can be represented as the lower envelope of a family of normalized dynamic convex risk measures. The link between dynamic monetary risk measures and dynamic star-shaped risk measures are established. Besides, the sensitivity and time consistency problems are also studied. A specific normalized time consistent dynamic star-shaped risk measures induced by $ g $-expectations are illustrated and discussed in detail.

Suggested Citation

  • Dejian Tian & Xunlian Wang, 2023. "Dynamic star-shaped risk measures and $g$-expectations," Papers 2305.02481, arXiv.org.
    • Handle: RePEc:arx:papers:2305.02481
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    References listed on IDEAS

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    1. Bingchu Nie & Dejian Tian & Long Jiang, 2024. "Set-valued Star-Shaped Risk Measures," Papers 2402.18014, arXiv.org.

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