Dynamic risk measures via backward doubly stochastic Volterra integral equations with jumps

Abstract

In this article, we study dynamic risk measures by means of backward doubly stochastic Volterra integral equations (BDSVIEs, for short) with jumps. We establish the well-posedness of BDSVIEs with jumps in the sense of M-solution and prove a comparison theorem of BDSVIEs with jumps. Finally, we study properties of dynamic risk measures induced by BDSVIEs with jumps. Our results extend the well-posedness and the comparison theorem of BDSVIEs without jumps to the setting with jumps, and extend dynamic risk measures induced by BSDEs, BDSDEs, and BSVIEs to the case of BDSVIEs with jumps.

KEYWORDS:

• Dynamic risk measures
• backward doubly stochastic Volterra integral equations with jumps
• comparison theorem

Mathematics Subject Classification (2010):

• 91B30
• 60G07
• 91B32
• 60J60

Additional information

Funding

Supported by the National Natural Science Foundation of China (No. 11901184) and the Natural Science Foundation of Hunan Province (No. 2020JJ5025).