Stochastic Calculus of Variations in Mathematical Finance

Stochastic Calculus of Variations in Mathematical Finance
Title Stochastic Calculus of Variations in Mathematical Finance PDF eBook
Author Paul Malliavin
Publisher Springer Science & Business Media
Total Pages 148
Release 2006-02-25
Genre Business & Economics
ISBN 3540307990

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Highly esteemed author Topics covered are relevant and timely

A Modern Theory of Random Variation

A Modern Theory of Random Variation
Title A Modern Theory of Random Variation PDF eBook
Author Patrick Muldowney
Publisher John Wiley & Sons
Total Pages 493
Release 2013-04-26
Genre Science
ISBN 1118345940

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A ground-breaking and practical treatment of probability and stochastic processes A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. In addition, an array of numerical examples and vivid illustrations showcase how the presented methods and applications can be undertaken at various levels of complexity. A Modern Theory of Random Variation is a suitable book for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensible resource for researchers and practitioners who are seeking new concepts, techniques and methodologies in data analysis, numerical calculation, and financial asset valuation. Patrick Muldowney, PhD, served as lecturer at the Magee Business School of the UNiversity of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.

Stochastic Calculus for Quantitative Finance

Stochastic Calculus for Quantitative Finance
Title Stochastic Calculus for Quantitative Finance PDF eBook
Author Alexander A Gushchin
Publisher Elsevier
Total Pages 208
Release 2015-08-26
Genre Mathematics
ISBN 0081004761

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In 1994 and 1998 F. Delbaen and W. Schachermayer published two breakthrough papers where they proved continuous-time versions of the Fundamental Theorem of Asset Pricing. This is one of the most remarkable achievements in modern Mathematical Finance which led to intensive investigations in many applications of the arbitrage theory on a mathematically rigorous basis of stochastic calculus. Mathematical Basis for Finance: Stochastic Calculus for Finance provides detailed knowledge of all necessary attributes in stochastic calculus that are required for applications of the theory of stochastic integration in Mathematical Finance, in particular, the arbitrage theory. The exposition follows the traditions of the Strasbourg school. This book covers the general theory of stochastic processes, local martingales and processes of bounded variation, the theory of stochastic integration, definition and properties of the stochastic exponential; a part of the theory of Lévy processes. Finally, the reader gets acquainted with some facts concerning stochastic differential equations. Contains the most popular applications of the theory of stochastic integration Details necessary facts from probability and analysis which are not included in many standard university courses such as theorems on monotone classes and uniform integrability Written by experts in the field of modern mathematical finance

Stochastic Calculus of Variations

Stochastic Calculus of Variations
Title Stochastic Calculus of Variations PDF eBook
Author Yasushi Ishikawa
Publisher Walter de Gruyter GmbH & Co KG
Total Pages 392
Release 2023-07-24
Genre Mathematics
ISBN 3110675323

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This book is a concise introduction to the stochastic calculus of variations for processes with jumps. The author provides many results on this topic in a self-contained way for e.g., stochastic differential equations (SDEs) with jumps. The book also contains some applications of the stochastic calculus for processes with jumps to the control theory, mathematical finance and so. This third and entirely revised edition of the work is updated to reflect the latest developments in the theory and some applications with graphics.

Stochastic Calculus for Finance

Stochastic Calculus for Finance
Title Stochastic Calculus for Finance PDF eBook
Author Marek Capiński
Publisher Cambridge University Press
Total Pages 187
Release 2012-08-23
Genre Business & Economics
ISBN 1107002648

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This book introduces key results essential for financial practitioners by means of concrete examples and a fully rigorous exposition.

Problems and Solutions in Mathematical Finance

Problems and Solutions in Mathematical Finance
Title Problems and Solutions in Mathematical Finance PDF eBook
Author Eric Chin
Publisher John Wiley & Sons
Total Pages 400
Release 2014-11-20
Genre Business & Economics
ISBN 1119966078

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Mathematical finance requires the use of advanced mathematicaltechniques drawn from the theory of probability, stochasticprocesses and stochastic differential equations. These areas aregenerally introduced and developed at an abstract level, making itproblematic when applying these techniques to practical issues infinance. Problems and Solutions in Mathematical Finance Volume I:Stochastic Calculus is the first of a four-volume set ofbooks focusing on problems and solutions in mathematicalfinance. This volume introduces the reader to the basic stochasticcalculus concepts required for the study of this important subject,providing a large number of worked examples which enable the readerto build the necessary foundation for more practical orientatedproblems in the later volumes. Through this application and byworking through the numerous examples, the reader will properlyunderstand and appreciate the fundamentals that underpinmathematical finance. Written mainly for students, industry practitioners and thoseinvolved in teaching in this field of study, StochasticCalculus provides a valuable reference book to complementone’s further understanding of mathematical finance.

Problems and Solutions in Mathematical Finance, Volume 1

Problems and Solutions in Mathematical Finance, Volume 1
Title Problems and Solutions in Mathematical Finance, Volume 1 PDF eBook
Author Eric Chin
Publisher John Wiley & Sons
Total Pages 404
Release 2014-11-10
Genre Business & Economics
ISBN 1119965837

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Mathematical finance requires the use of advanced mathematical techniques drawn from the theory of probability, stochastic processes and stochastic differential equations. These areas are generally introduced and developed at an abstract level, making it problematic when applying these techniques to practical issues in finance. Problems and Solutions in Mathematical Finance Volume I: Stochastic Calculus is the first of a four-volume set of books focusing on problems and solutions in mathematical finance. This volume introduces the reader to the basic stochastic calculus concepts required for the study of this important subject, providing a large number of worked examples which enable the reader to build the necessary foundation for more practical orientated problems in the later volumes. Through this application and by working through the numerous examples, the reader will properly understand and appreciate the fundamentals that underpin mathematical finance. Written mainly for students, industry practitioners and those involved in teaching in this field of study, Stochastic Calculus provides a valuable reference book to complement one’s further understanding of mathematical finance.