The numerical solution of stochastic differential equations is becoming an in- dispensible worktool in a multitude of disciplines, bridging a long-standing gap between the well advanced theory of stochastic differential equations and its application to specific examples. This has been made possible by the much greater accessibility to high-powered computers at low-cost combined with the availability of new, effective higher order numerical schemes for stochastic dif- ferential equations. Many hitherto intractable problems can now be tackled successfully and more realistic modelling with...

The aim of this book is to provide an accessible introduction to stochastic differ- ential equations and their applications together with a systematic presentation of methods available for their numerical solution. During the past decade there has been an accelerating interest in the de- velopment of numerical methods for stochastic differential equations (SDEs). This activity has been as strong in the engineering and physical sciences as it has in mathematics, resulting inevitably in some duplication of effort due to an unfamiliarity with the developments in other disciplines. Much of the...

The aim of this book is to provide an accessible introduction to stochastic differ- ential equations and their applications together with a systematic presentation of methods available for their numerical solution. During the past decade there has been an accelerating interest in the de- velopment of numerical methods for stochastic differential equations (SDEs). This activity has been as strong in the engineering and physical sciences as it has in mathematics, resulting inevitably in some duplication of effort due to an unfamiliarity with the developments in other disciplines. Much of the...

In recent years products based on ?nancial derivatives have become an ind- pensabletoolforriskmanagersandinvestors. Insuranceproductshavebecome part of almost every personal and business portfolio. The management of - tual and pension funds has gained in importance for most individuals. Banks, insurance companies and other corporations are increasingly using ?nancial and insurance instruments for the active management of risk. An increasing range of securities allows risks to be hedged in a way that can be closely t- lored to the speci?c needs of particular investors and companies. The...

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...

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.

This volume provides an introduction to stochastic differential equations with jumps, in both theory and application. The book is accessible and contains many new results on numerical methods but also innovative methodologies in quantitative finance.