Functionals of Multidimensional Diffusions with Applications to Finance 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.