Offers new or improved methods for dealing with volatility of the financial marketIncludes concise discussion of modelling, analysis and numerical solution methods for nonlinear Black-Scholes equations Several sections devoted to GPU programming techniques for solving financial problems Special chapter on software includes the Computational Finance Toolbox that provides insights to the detailed implementation of the proposed methods

Autorentext
Matthias Ehrhardt is coordinator of ITN STRIKE.and professor of mathematics at University of Wuppertal, Germany.

Zusammenfassung

This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector.

The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models.

In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techniques are now essential to the majority of present-day applications in the financial industry.

Special attention is devoted to a uniform methodology for both testing the latest achievements and simultaneously educating young PhD students. Most of the mathematical codes are linked into a novel computational finance toolbox, which is provided in MATLAB and PYTHON with an open access license. The book offers a valuable guide for researchers in computational finance and related areas, e.g. energy markets, with an interest in industrial mathematics.

Inhalt
Part I Modelling.- Part II Analysis.- Part III Transformation Methods and Special Discretizations.- Part IV Numerical Methods in Finance.- Part V Compact FDMs and Splitting Schemes.- Part VI Scientific Computing.- Part VII High Performance Computing.- Part VIII Software.