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.

Functionals of Multidimensional Diffusions with Applications to Finance (Bocconi & Springer Series, 5)

Business & Money

Platen, Eckhard

Baldeaux, Jan

Economics

Springer

A framework for financial market modeling, the benchmark approach extends beyond standard risk neutral pricing theory. It permits a unified treatment of portfolio optimization, derivative pricing, integrated risk management and insurance risk modeling. This book presents the necessary mathematical tools, followed by a thorough introduction to financial modeling under the benchmark approach, explaining various quantitative methods for the fair pricing and hedging of derivatives.

A Benchmark Approach to Quantitative Finance (Springer Finance)

Heath, David

The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP

Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability, 23)

Kloeden, Peter E.

Education & Reference

This book provides an easily accessible, computationally-oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations. It also creates an intuitive understanding of the necessary theoretical background. Software containing programs for over 100 problems is available online.

Numerical Solution of SDE Through Computer Experiments (Universitext)

Science & Math

Kloeden, Peter Eris

Schurz, Henri

Mathematics

Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability)

Kloeden, Peter E. E.

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden &amp; Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.

Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Stochastic Modelling and Applied Probability, 64)

Bruti-Liberati, Nicola

Finance

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.

See the best price to sell, buy, or rent books by Platen, Eckhard. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Platen, Eckhard

See the best price to sell, buy, or rent books by Platen, Eckhard. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Functionals of Multidimensional Diffusions with Applications to Finance (Bocconi & Springer Series, 5)

A Benchmark Approach to Quantitative Finance (Springer Finance)

Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability, 23)

Numerical Solution of SDE Through Computer Experiments (Universitext)

A Benchmark Approach to Quantitative Finance (Springer Finance)

Numerical Solution of Stochastic Differential Equations (Stochastic Modelling and Applied Probability)

Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Stochastic Modelling and Applied Probability, 64)

Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Stochastic Modelling and Applied Probability, 64)