Malliavin calculus provides an infinite-dimensional differential
calculus in the context of continuous paths stochastic processes.
The calculus includes formulae of integration by parts and Sobolev
spaces of differentiable functions defined on a probability space.
This new book, demonstrating the relevance of Malliavin calculus for
Mathematical Finance, starts with an exposition from scratch of
Greeks (price sensitivities) are reinterpreted in terms of Malliavin
Integration by parts formulae provide stable Monte Carlo schemes for
numerical valuation of digital options.
Finite-dimensional projections of infinite-dimensional Sobolev spaces
lead to Monte Carlo computations of conditional expectations useful
for computing American options.
Weak convergence of numerical integration of SDE is interpreted
as a functional belonging to a Sobolev space of negative order.
Insider information is expressed as an infinite-dimensional drift.
The last chapter gives an introduction to the same objects
in the context of jump processes where incomplete markets appear.