Acta mathematica scientia,Series B ›› 2023, Vol. 43 ›› Issue (3): 1365-1381.doi: 10.1007/s10473-023-0321-2

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ANTICIPATED BACKWARD STOCHASTIC VOLTERRA INTEGRAL EQUATIONS WITH JUMPS AND APPLICATIONS TO DYNAMIC RISK MEASURES*

Liangliang Mia1, Yanhong Chen2,†, Xiao Xiao3, Yijun Hu4   

  1. 1. School of Mathematics and Information Technology, Jiangsu Second Normal University, Nanjing 210013, China;
    2. College of Finance and Statistics, Hunan University, Changsha 410082, China;
    3. School of Mathematics and Information Technology, Jiangsu Second Normal University, Nanjing 210013, China;
    4. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2020-09-17 Revised:2022-01-18 Online:2023-06-25 Published:2023-06-06
  • Contact: Yanhong Chen, E-mail: yhchen@hnu.edu.cn
  • About author:Liangliang Miao, E-mail: liangliangmiao@whu.edu.cn;Xiao Xiao, E-mail: primexxiao@163.com;Yijun Hu, E-mail: yjhu.math@whu.edu.cn
  • Supported by:
    This paper was supported by the National Natural Science Foundation of China (11901184, 11771343) and the Natural Science Foundation of Hunan Province (2020JJ5025).

Abstract: In this paper, we focus on anticipated backward stochastic Volterra integral equations (ABSVIEs) with jumps. We solve the problem of the well-posedness of so-called M-solutions to this class of equation, and analytically derive a comparison theorem for them and for the continuous equilibrium consumption process. These continuous equilibrium consumption processes can be described by the solutions to this class of ABSVIE with jumps. Motivated by this, a class of dynamic risk measures induced by ABSVIEs with jumps are discussed.

Key words: anticipated backward stochastic Volterra integral equations, comparison theorems, dynamic risk measures

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