The Malliavin calculus, named after Paul Malliavin, is a theory of variational stochastic calculus. In other words it provides the mechanics to compute derivatives of random variables. Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas. ... Stochastic calculus is a branch of mathematics that operates on stochastic processes. ... In mathematics, the derivative is one of the two central concepts of calculus. ... A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result. ...

A useful feature is the ability to perform integration by parts on random variables. Major uses are in financial mathematics to compute sensitivities of financial derivatives (also known as the Greeks). In calculus, and more generally in mathematical analysis, integration by parts is a rule that transforms the integral of products of functions into other, possibly simpler, integrals. ... A random variable can be thought of as the numeric result of operating a non-deterministic mechanism or performing a non-deterministic experiment to generate a random result. ... Mathematical finance is the branch of applied mathematics concerned with the financial markets. ... A derivative is a financial contract whose payoffs over a period of time are derived from the performance of assets, interest rates, exchange rates, or indices. ...

External links

• Bernt Oksendal. An Introduction To Malliavin Calculus With Applications To Economics
• Peter K. Friz. An Introduction to Malliavin Calculus