Dynamic risk measure for BSVIE with jumps and semimartingale issues

Abstract

Risk measure is a fundamental concept in finance and in the insurance industry. It is used to adjust life insurance rates. In this article, we will study dynamic risk measures by means of backward stochastic Volterra integral equations (BSVIEs) with jumps. We prove a comparison theorem for such a type of equations. Since the solution of a BSVIEs is not a semimartingale in general, we will discuss some particular semimartingale issues.

Keywords:

• Brownian motion
• compensated Poisson random measure
• backward stochastic Volterra integral equation
• risk measure
• semimartingale

MSC(2010):

• 60H07
• 60H20
• 60H30
• 45D05
• 45R05

Acknowledgments

We would like to thank Prof. Yong for pointing out the reference [21] which helped us to improve the article. We also want to thank Prof. Rosazza Gianin for helpful comments. Part of this work has been done while the author is visiting the University of Alberta, Canada and I would like to thank Prof. Hu for the hospitality and his comments during my talk.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was carried out with support of the Norwegian Research Council within the research project Challenges in Stochastic Control/project number 250768F20.