2021/12/28 by Christian Houdré, Houdré, Christian, Jorge Víquez +1
Economics, Econometrics and Finance · Social Sciences · Decision Sciences · #Stochastic processes and financial applications #Insurance, Mortality, Demography, Risk Management #Probability and Risk Models
paper · pdf · doi:10.48550/arxiv.2112.14221
Several versions of Itô's formula have been obtained in the context of the functional stochastic calculus. Here, we revisit this topic in two ways. First, by defining a notion of derivative along a functional, we extend the setting of the (semimartingale) functional Itô's formula and corresponding calculus. Second, for Lévy processes, an optimal local-time based Itô's formula is obtained. Some quick applications are then given.