# Brownian Motion Calculus

## Ubbo F. Wiersema

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Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites.  Summary slides for revision and teaching can be found on the book website.

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Brownian Motion Calculus

Ubbo Wiersema

Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. The sequence of chapters starts with a description of Brownian motion, the random process which serves as the basic driver of the irregular behaviour of financial quantities. That exposition is based on the easily understood discrete random walk. Thereafter the gains from trading in a random environment are formulated in a discrete-time setting. The continuous-time equivalent requires a new concept, the Itō stochastic integral. Its construction is explained step by step, using the so-called norm of a random process (its magnitude), of which a motivated exposition is given in an Annex. The next topic is Itō’s formula for evaluating stochastic integrals; it is the random process counter part of the well known Taylor formula for functions in ordinary calculus. Many examples are given. These ingredients are then used to formulate some well established models for the evolution of stock prices and interest rates, so-called stochastic differential equations, together with their solution methods. Once all that is in place, two methodologies for option valuation are presented. One uses the concept of a change of probability and the Girsanov transformation, which is at the core of financial mathematics. As this technique is often perceived as a magic trick, particular care has been taken to make the explanation elementary and to show numerous applications. The final chapter discusses how computations can be made more convenient by a suitable choice of the so-called numeraire. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website www.wiley.com/go/brownianmotioncalculus.

UBBO WIERSEMA was educated in Applied Mathematics at Delft, in Operations Research at Berkeley, and in Financial Economics and Financial Mathematics at the London School of Economics. He joined The Business School for Financial Markets (the ICMA Centre) at the University of Reading, UK, in 1997, to develop and teach its curriculum in Quantitative Finance. Prior to that, he was a derivatives mathematician at the merchant bank Robert Fleming in the City of London. Before that his career was focused in Operations Research in the US and Europe.

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## 1.Brownian Motion Calculus (Paperback)

Editore: John Wiley and Sons Ltd, United Kingdom (2008)
ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro John Wiley and Sons Ltd, United Kingdom, 2008. Paperback. Condizione libro: New. 1. Auflage. Language: English . Brand New Book. Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website. Codice libro della libreria AAZ9780470021705

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## 2.Brownian Motion Calculus

Editore: Wiley 2008-04-15, Chichester (2008)
ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro Wiley 2008-04-15, Chichester, 2008. paperback. Condizione libro: New. Codice libro della libreria 9780470021705

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## 3.Brownian Motion Calculus

Editore: John Wiley & Sons 2008-08-01 (2008)
ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro John Wiley & Sons 2008-08-01, 2008. Condizione libro: New. Brand new book, sourced directly from publisher. Dispatch time is 24-48 hours from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-GRD-00656700

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## 4.Brownian Motion Calculus (Paperback)

Editore: John Wiley and Sons Ltd, United Kingdom (2008)
ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro John Wiley and Sons Ltd, United Kingdom, 2008. Paperback. Condizione libro: New. 1. Auflage. Language: English . Brand New Book. Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website. Codice libro della libreria AAZ9780470021705

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## 5.Brownian Motion Calculus

Editore: John Wiley and#38; Sons (2008)
ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro John Wiley and#38; Sons, 2008. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria FW-9780470021705

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## 6.Brownian Motion Calculus

Editore: John Wiley and Sons Ltd
ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro John Wiley and Sons Ltd. Paperback. Condizione libro: new. BRAND NEW, Brownian Motion Calculus, Ubbo F. Wiersema, Brownian Motion Calculus presents the basics of Stochastic Calculus with a focus on the valuation of financial derivatives. It is intended as an accessible introduction to the technical literature. A clear distinction has been made between the mathematics that is convenient for a first introduction, and the more rigorous underpinnings which are best studied from the selected technical references. The inclusion of fully worked out exercises makes the book attractive for self study. Standard probability theory and ordinary calculus are the prerequisites. Summary slides for revision and teaching can be found on the book website. Codice libro della libreria B9780470021705

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## 7.Brownian Motion Calculus (Paperback)

ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro Condizione libro: New. Bookseller Inventory # ST0470021705. Codice libro della libreria ST0470021705

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## 8.Brownian Motion Calculus

Editore: John Wiley and Sons Ltd (2008)
ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro John Wiley and Sons Ltd, 2008. Condizione libro: New. 2008. 1st Edition. Paperback. There are not many calculus books that are very accessible to students without a strong mathematical background and the large majority of financial derivatives students do not have a strong quantitative background. This book provides a short introduction to the subject with examples of its use in mathematical finance e. g pricing of derivatives. Num Pages: 330 pages, Illustrations. BIC Classification: PDE; PHF. Category: (P) Professional & Vocational. Dimension: 157 x 231 x 19. Weight in Grams: 488. . . . . . . Codice libro della libreria V9780470021705

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## 9.Brownian Motion Calculus

Editore: John Wiley and Sons Ltd
ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro John Wiley and Sons Ltd. Condizione libro: New. 2008. 1st Edition. Paperback. There are not many calculus books that are very accessible to students without a strong mathematical background and the large majority of financial derivatives students do not have a strong quantitative background. This book provides a short introduction to the subject with examples of its use in mathematical finance e. g pricing of derivatives. Num Pages: 330 pages, Illustrations. BIC Classification: PDE; PHF. Category: (P) Professional & Vocational. Dimension: 157 x 231 x 19. Weight in Grams: 488. . . . . . Books ship from the US and Ireland. Codice libro della libreria V9780470021705

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## 10.Brownian Motion Calculus

Editore: John Wiley & Sons (2008)
ISBN 10: 0470021705 ISBN 13: 9780470021705
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Descrizione libro John Wiley & Sons, 2008. Condizione libro: New. book. Codice libro della libreria ria9780470021705_rkm

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