# Dynamic risk measure for BSVIE with jumps and semimartingale issues

## TL;DR

This paper develops a framework for dynamic risk measures using backward stochastic Volterra integral equations with jumps, addressing semimartingale challenges and establishing a comparison theorem.

## Contribution

It introduces a comparison theorem for BSVIEs with jumps and discusses semimartingale issues, advancing the mathematical understanding of risk measures.

## Key findings

- Established a comparison theorem for BSVIEs with jumps
- Analyzed semimartingale properties of BSVIE solutions
- Enhanced mathematical tools for dynamic risk assessment

## Abstract

Risk measure is a fundamental concept in finance and in the insurance industry, it is used to adjust life insurance rates. In this current paper, 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.