Linear Backward Stochastic Differential Equations with Gaussian Volterra processes

TL;DR

This paper derives explicit solutions for linear backward stochastic differential equations driven by Gaussian Volterra processes, linking them to PDEs via a Feynman-Kac formula, with applications in finance.

Contribution

It introduces explicit solutions for BSDEs driven by Gaussian Volterra processes and connects them to PDEs using Malliavin calculus and Feynman-Kac formulas.

Findings

Explicit solutions for BSDEs driven by Gaussian Volterra processes.

Connection between BSDEs and PDEs via Feynman-Kac formula.

Application to self-financing trading strategies.

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.