Functional Itô Calculus
Functional Itô calulus was firstly introduced in the seminal paper by Bruno Dupire in 2009. Since then, numerous contributions to extend the theory as well as the applications were made.
This theory extends the classical Itô stochastic calculus to functionals of the current history of a given process, and hence such theory provides an excellent tool to the study of path-dependence.
My research contributions in this topic are:
An alternative approach to the classical Malliavin calculus for the computation of sensitivities, also called Greeks, of path-dependent derivatives prices using fucntional Itô calculus;
Definition and analysis of the Lie bracket (or commutator) of the time and space functional derivatives and its connection to path-dependence;
Perturbation analysis for path-dependent functionals;
Functional Tanaka formula.