Backward stochastic Volterra integral equations associated with a Levy process and applications

Details Backward stochastic Volterra integral equations associated with a Levy process and applications Backward stochastic Volterra integral equations associated with a Levy process and applications

2011-06-30

arxiv.org/abs/1106.6129v1

Mathematics

Probability

Scientific paper

In this paper, we study a class of backward stochastic Volterra integral equations driven by Teugels martingales associated with an independent L\'{e}vy process and an independent Brownian motion (BSVIELs). We prove the existence and uniqueness as well as stability of the adapted M-solutions for those equations. Moreover, a duality principle and then a comparison theorem are established. As an application, we derive a class of dynamic risk measures by means of M-solutions of certain BSVIELs.

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