Malliavin calculus

Summary

Malliavin calculus is a differential calculus for random variables that are functions of a Brownian motion path. Its basic operator is the Malliavin derivative $D$, which measures how a random variable changes when the path is perturbed in directions of finite energy. Its adjoint is the Skorokhod integral, which extends the Itô integral to integrands that are not adapted. It is used to prove that laws of solutions of stochastic differential equations have smooth densities, and to compute sensitivities in finance.