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Linear Volterra backward stochastic integral equations
Authors:Yaozhong Hu  Bernt Øksendal
Affiliation:1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1;2. Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, N–0316 Oslo, Norway
Abstract:We present an explicit solution triplet (Y,Z,K) to the backward stochastic Volterra integral equation (BSVIE) of linear type, driven by a Brownian motion and a compensated Poisson random measure. The process Y is expressed by an integral whose kernel is explicitly given. The processes Z and K are expressed by Hida–Malliavin derivatives involving Y.
Keywords:60H07  60H20  60H30  45D05  45R05  Brownian motion  Compensated Poisson random measure  Volterra type backward stochastic differential equation  Linear equation  Explicit solution  Hida–Malliavin derivative
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