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

Dejian Tian; Xunlian Wang

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arXiv · 2305.02481

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

Dejian Tian·Xunlian Wang

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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.

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Dejian Tian, Xunlian Wang. 2023-05-04. Dynamic star-shaped risk measures and $g$-expectations. https://arxiv.org/abs/2305.02481

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