1652993940

Functionals of Multidimensional Diffusions with Applications to Finance / by Jan Baldeaux, Eckhard Platen

Englisch

Cham ; s.l. : Springer International Publishing ; Imprint: Springer, 2013

Online-Ressource (XXIII, 425 p. 38 illus., 27 illus. in color, online resource)

Description based upon print version of record

Druckausg.: Functionals of multidimensional diffusions with applications to finance. - Cham : Springer, 2013. - XXIII, 425 S.

978-3-319-00747-2

Weitere Ausgaben: 978-3-319-00746-5 (Druckausgabe)

DOI: 10.1007/978-3-319-00747-2

1 A Benchmark Approach to Risk Management2 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.

*Diffusionsprozess / Finanzmathematik

*Diffusionsprozess / Finanzmathematik

*Finance ; Mathematics ; Economics, Mathematical . ; Macroeconomics. ; Applied mathematics. ; Engineering mathematics. ; Mathematics ; Finance

Klassifikation der Library of Congress: HB135-147

Dewey Dezimal-Klassifikation: 519;

Regensburger Verbund-Klassifikation: SK 820: SA-SP Mathematik / SK Monografien / SK 800 Wahrscheinlichkeitstheorie / Stochastische Prozesse

bisacsh: BUS027000

Book Industry Communication: KF

bisacsh: MAT003000

Mathematics Subject Classification: *60-01

Mathematics Subject Classification: 60J60

Mathematics Subject Classification: 60J70

Mathematics Subject Classification: 91Gxx

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.

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.

https://zbmath.org/?q=an:1401.60001 [Zentralblatt MATH]

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https://doi.org/10.1007/978-3-319-00747-2 [E-books (Springer)]