Product and Moment Formulas for Iterated Stochastic Integrals (associated with Lévy Processes)

Abstract

In this paper, we obtain explicit product and moment formulas for products of iterated integrals generated by families of square integrable martingales associated with an arbitrary Lévy process. We propose a new approach applying the theory of compensated-covariation stable families of martingales. Our main tool is a representation formula for products of elements of a compensated-covariation stable family, which enables to consider Lévy processes, with both jumps and Gaussian part.