Convex comparison inequalities for non-Markovian stochastic integrals
Résumé
We derive convex comparison inequalities for stochastic integrals of the form integral(T)(0)sigma(t)*d (B) over cap (t) and integral(T)(0)sigma(t)dB(t), where 0 <= sigma(t)* <= sigma(t) are adapted processes with respect to the filtration generated by a standard Brownian motion (B-t)(t is an element of[0,T]), and ((B) over cap (t))(t is an element of[0,T]) is an independent Brownian motion. Our method uses forward-backward stochastic integration and the Malliavin calculus, and is also applied to jump-diffusion processes.