Linear Backward Stochastic Differential Equations with Gaussian Volterra processes
Probability
2019-12-03 v1
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.
Keywords
Cite
@article{arxiv.1912.00054,
title = {Linear Backward Stochastic Differential Equations with Gaussian Volterra processes},
author = {Habiba Knani and Marco Dozzi},
journal= {arXiv preprint arXiv:1912.00054},
year = {2019}
}