Functionals of multidimensional diffusions with applications to finance. (English) Zbl 1401.60001

Baldeaux, Jan; Platen, Eckhard

Bocconi & Springer Series 5. Cham: Springer; Milano: Bocconi University Press (ISBN 978-3-319-00746-5/hbk; 978-3-319-00747-2/ebook). xxiii, 425 p. (2013).

The textbook at hand focuses on “tractable multidimensional models with functionals that have explicit solutions”. Particular emphasis is placed on transformations of squares of Brownian motion, such as multidimensional Bessel, square-root, or affine processes. These models are applied to a variety of financial problems, with a particular emphasis on the “benchmark approach” pioneered by the second author. The book also covers in detail numerical techniques such exact and almost exact simulation, transform methods, and quasi-Monte Carlo schemes. Moreover, it contains a self-contained summary of the tools from stochastic calculus that are used in the main body of the text.

Reviewer: Johannes Muhle-Karbe (Pittsburgh)

MSC:

60-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60J60	Diffusion processes
60J70	Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
91Gxx	Actuarial science and mathematical finance

Keywords:

multidimensional diffusions; functionals; closed-form; numerical methods; applications to finance

Software:

AS 275