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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}
}
R2 v1 2026-06-23T12:31:35.689Z