Linear backward stochastic differential equations with Gaussian Volterra processes
Volume 7, Issue 4 (2020), pp. 415–433
Pub. online: 3 December 2020
Type: Research Article
Open Access
Open Access
Received
9 April 2020
9 April 2020
Revised
8 September 2020
8 September 2020
Accepted
1 November 2020
1 November 2020
Published
3 December 2020
3 December 2020
Abstract
Explicit solutions for a class of linear backward stochastic differential equations (BSDE) driven by Gaussian Volterra processes are given. These processes include the multifractional Brownian motion and the multifractional Ornstein-Uhlenbeck process. By an Itô formula, proven in the context of Malliavin calculus, the BSDE is associated to a linear second order partial differential equation with terminal condition whose solution is given by a Feynman-Kac type formula.
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