Linear Backward Stochastic Differential Equations with Gaussian Volterra processes

Habiba Knani; Marco Dozzi

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arXiv · 1912.00054

Linear Backward Stochastic Differential Equations with Gaussian Volterra processes

Habiba Knani·Marco Dozzi

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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 It\^o 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. An application to self-financing trading strategies is discussed.

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Habiba Knani, Marco Dozzi. 2019-11-29. Linear Backward Stochastic Differential Equations with Gaussian Volterra processes. https://arxiv.org/abs/1912.00054

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