TY  - BOOK
AU  - Baldeaux,Jan
AU  - Platen,Eckhard
ED  - SpringerLink (Online service)
TI  - Functionals of Multidimensional Diffusions with Applications to Finance
T2  - Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics,
SN  - 9783319007472
AV  - HB135-147 
U1  - 519 23
PY  - 2013///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematics
KW  - Applied mathematics
KW  - Engineering mathematics
KW  - Economics, Mathematical
KW  - Macroeconomics
KW  - Quantitative Finance
KW  - Macroeconomics/Monetary Economics//Financial Economics
KW  - Applications of Mathematics
N1  - 1 A Benchmark Approach to Risk Management -- 2 Functionals of Wiener Processes -- 3 Functionals of Squared Bessel Processes -- 4 Lie Symmetry Group Methods -- 5 Transition Densities via Lie Symmetry Methods -- 6 Exact and Almost Exact Simulation -- 7 Affine Diffusion Processes on the Euclidean Space -- 8 Pricing Using Affine Diffusions -- 9 Solvable Affine Processes on the Euclidean State Space -- 10 An Introduction to Matrix Variate Stochastics -- 11 Wishart Processes -- 12 Monte Carlo and Quasi-Monte Carlo Methods -- 13 Computational Tools -- 14 Credit Risk under the Benchmark Approach -- A Continuous Stochastic Processes -- B Time-Homogeneous Scalar Diffusions -- C Detecting Strict Local Martingales
N2  - This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions
UR  - http://dx.doi.org/10.1007/978-3-319-00747-2
ER  -