Skip to content
All library documents

Linear BSDEs with Gaussian Volterra Processes and Trading Applications

Article arXiv papers · Author: Habiba Knani et al.
Read the original

Summary

This document presents explicit solutions for a class of linear backward stochastic differential equations driven by Gaussian Volterra processes. The processes discussed include multifractional Brownian motion and multifractional Ornstein-Uhlenbeck processes, extending the framework beyond more standard Brownian drivers.

Using an Itô formula established through Malliavin calculus, the work connects the BSDE to a linear second-order partial differential equation with a terminal condition. A Feynman-Kac type representation gives the PDE solution, and the document notes an application to self-financing trading strategies. The description provides no details about the trading setup, empirical evaluation, or practical performance, so it establishes a mathematical connection rather than evidence for a particular trading advantage.

Key ideas

  • The work gives explicit solutions for a class of linear BSDEs driven by Gaussian Volterra processes.
  • Examples of the driving processes include multifractional Brownian motion and multifractional Ornstein-Uhlenbeck processes.
  • A Malliavin-calculus Itô formula links the BSDE to a linear second-order PDE.
  • A Feynman-Kac type formula represents the PDE solution, with an application to self-financing strategies.

Tags

StatisticsDerivatives pricing
Full text
# Linear Backward Stochastic Differential Equations with Gaussian Volterra processes


# Linear Backward Stochastic Differential Equations with Gaussian Volterra processes









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. An application to self-financing trading strategies is discussed.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.