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Error Calculus for Finance and Physics : The Language of Dirichlet Forms - Nicolas Bouleau

Error Calculus for Finance and Physics

The Language of Dirichlet Forms

Hardcover Published: 15th December 2003
ISBN: 9783110180367
Number Of Pages: 244
For Ages: 22+ years old

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Many recent advances in modelling within the applied sciences and engineering have focused on the increasing importance of sensitivity analyses. For a given physical, financial or environmental model, increased emphasis is now placed on assessing the consequences of changes in model outputs that result from small changes or errors in both the hypotheses and parameters. The approach proposed in this book is entirely new and features two main characteristics. Even when extremely small, errors possess biases and variances. The methods presented here are able, thanks to a specific differential calculus, to provide information about the correlation between errors in different parameters of the model, as well as information about the biases introduced by non-linearity. The approach makes use of very powerful mathematical tools (Dirichlet forms), which allow one to deal with errors in infinite dimensional spaces, such as spaces of functions or stochastic processes. The method is therefore applicable to non-elementary models along the lines of those encountered in modern physics and finance. This text has been drawn from presentations of research done over the past ten years and that is still ongoing. The work was presented in conjunction with a course taught jointly at the Universities of Paris 1 and Paris 6. The book is intended for students, researchers and engineers with good knowledge in probability theory.

Industry Reviews

"[...] interesting book [...]"
Alexander Schied in: Zentralblatt MATH 12/2007

Intuitive introduction to error structuresp. 1
Strongly-continuous semigroups and Dirichlet formsp. 17
Error structuresp. 32
Images and products of error structuresp. 51
Sensitivity analysis and error calculusp. 67
Error structures on fundamental spaces spacep. 93
Application to financial modelsp. 137
Applications in the field of physicsp. 187
Indexp. 231
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9783110180367
ISBN-10: 3110180367
Series: de Gruyter Expositions in Mathematics
Audience: General
For Ages: 22+ years old
Format: Hardcover
Language: English
Number Of Pages: 244
Published: 15th December 2003
Country of Publication: DE
Dimensions (cm): 24.41 x 16.99  x 1.6
Weight (kg): 0.55