English

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 g g -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}
}

Comments

21 pages

R2 v1 2026-06-28T10:25:09.522Z