Abstract
This paper studies Backward Stochastic Volterra Integral Equations (BSVIEs) driven by finite state, continuous time Markov chains. First, the existence and uniqueness of the solutions to two types of BSVIEs are established. Second, some scalar and vector comparison theorems are given. Finally, the applications of BSVIEs to a linear-quadratic optimal control problem and time-inconsistent coherent risk measures are presented.
Acknowledgements
The author would like to thank two anonymous referees for their valuable comments and suggestions to improve on earlier versions of this paper, and thank Dr Tianxiao Wang for valuable discussions on BSVIEs.
Notes
No potential conflict of interest was reported by the author.
1 The arguments in that paper still hold for the BSVIEs driven by Markov chains.