Functionals of Multidimensional Diffusions with Applications to Finance

This research monograph provides an introduction to tractable multidimensional diffusion models. It also offers an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals.

Provides the reader in a systematic way with the ability to derive explicit formulas for functionals of multidimensional diffusions Special unique chapters on Lie symmetry group methods and matrix valued Wishart processes Provides the most recent introduction to the benchmark approach to finance pioneered by Platen and co-authors The reader finds readily applicable exact simulation methods for various multidimensional diffusion processes? Includes supplementary material: sn.pub/extras

Autorentext
Professor Eckhard Platen is a joint appointment between the School of Finance and Economics and the Department of Mathematical Sciences to the 1997 created Chair in Quantitative Finance at the University of Technology Sydney. Prior to this appointment he was Founding Head of the Centre for Financial Mathematics at the Institute of Advanced Studies at the Australian National University in Canberra. He completed a PhD in Mathematics at the Technical University in Dresden in 1975 and obtained in 1985 his Dr. sc. from the Academy of Sciences in Berlin, where he headed at the Weierstrass Institute the Sector of Stochastics. He is co-author of two successful books on Numerical Methods for Stochastic Differential Equations, published by Springer Verlag, and has authored more than 100 research papers in quantitative finance and mathematics.

Inhalt
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.