Convex comparison inequalities for non-Markovian stochastic integrals

Abstract

We derive convex comparison inequalities for stochastic integrals of the form and , where are adapted processes with respect to the filtration generated by a standard Brownian motion , and is an independent Brownian motion. Our method uses forward–backward stochastic integration and the Malliavin calculus, and is also applied to jump–diffusion processes.

Keywords:

• convex concentration
• Malliavin calculus
• forward–backward stochastic calculus
• jump–diffusion processes

Mathematics Subject Classification::

• 60E15
• 60H05
• 60G44
• 60G55

Acknowledgements

The third author acknowledges the financial support from NTU Start-Up Grant M58110087.