LEADER 03384nam 2200517Ia 450 001 9910438145603321 005 20200520144314.0 010 $a3-319-00747-5 024 7 $a10.1007/978-3-319-00747-2 035 $a(OCoLC)857279861 035 $a(MiFhGG)GVRL6WOM 035 $a(CKB)2670000000533725 035 $a(MiAaPQ)EBC1398591 035 $a(EXLCZ)992670000000533725 100 $a20130819d2013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aFunctionals of multidimensional diffusions with applications to finance /$fJan Baldeaux, Eckhard Platen 205 $a1st ed. 2013. 210 $aCham ;$aNew York $cBocconi University Press / Springer$dc2013 215 $a1 online resource (xxiii, 425 pages) $cillustrations (some color) 225 0 $aBocconi & Springer series 300 $a"ISSN: 2039-1471." 311 $a3-319-00746-7 311 $a3-319-03334-4 320 $aIncludes bibliographical references and index. 327 $a1 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. 330 $aThis research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions. 410 0$aBocconi & Springer series ;$vvolume 5. 606 $aFinancial instruments 606 $aFinance 615 0$aFinancial instruments. 615 0$aFinance. 676 $a519.233 700 $aBaldeaux$b Jan$01063021 701 $aPlaten$b Eckhard$021625 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438145603321 996 $aFunctionals of multidimensional diffusions with applications to finance$94194424 997 $aUNINA