Stochastic Calculus of Variations in Mathematical Finance

This extensive and up-to-date text demonstrates the relevance of Malliavin calculus for Mathematical Finance. It starts with an exposition from scratch of this theory. Greeks (price sensitivities) are reinterpreted in terms of Malliavin calculus. 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. 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.

Extremely famous author. The Stochastic calculus of variations is usually denoted as the "Malliavin Calculus" Very up-to-date topics (see "contents") Self-contained, with a view to numerical applications While Malliavin's writing is difficult, his co-author will make the content more amenable to readers Includes supplementary material: sn.pub/extras

Contenu
Gaussian Stochastic Calculus of Variations.- Computation of Greeks and Integration by Parts Formulae.- Market Equilibrium and Price-Volatility Feedback Rate.- Multivariate Conditioning and Regularity of Law.- Non-Elliptic Markets and Instability in HJM Models.- Insider Trading.- Asymptotic Expansion and Weak Convergence.- Stochastic Calculus of Variations for Markets with Jumps.