Dynamic star-shaped risk measures and $g$-expectations
Risk Management
2023-05-05 v1
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 -expectations are illustrated and discussed in detail.
Keywords
Cite
@article{arxiv.2305.02481,
title = {Dynamic star-shaped risk measures and $g$-expectations},
author = {Dejian Tian and Xunlian Wang},
journal= {arXiv preprint arXiv:2305.02481},
year = {2023}
}
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21 pages