From Measures to Itô Integrals
 Author/Creator
 Kopp, Ekkehard (Peter Ekkehard), 1944 author.
 Language
 English.
 Imprint
 Cambridge ; New York : Cambridge University Press, 2011.
 Physical description
 vii, 120 pages : illustrations ; 22 cm.
 Series
 AIMS library series.
Access
Available online

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QA312 .K5867 2011

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QA312 .K5867 2011
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Contents/Summary
 Bibliography
 Includes bibliographical references (pages 118) and index.
 Contents

 Machine generated contents note: Preface; 1. Probability and measure; 2. Measures and distribution functions; 3. Measurable functions/random variables; 4. Integration and expectation; 5. Lpspaces and conditional expectation; 6. Discretetime martingales; 7. Brownian motion; 8. Stochastic integrals; Bibliography; Index.
 Summary
 "From Measures to Itô Integrals gives a clear account of measure theory, leading via L2theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduatelevel courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus" Provided by publisher.
 "Undergraduate mathematics syllabi vary considerably in their coverage of measuretheoretic probability theory, so beginning graduates often find substantial gaps in their background when attending modules in advanced analysis, stochastic processes and applications. This text seeks to fill some of these gaps concisely. The exercises form an integral part of the text. The material arose from my experience of teaching AIMS students between 2004 and 2007, of which I retain many fond memories. The AIMS series format allows few explorations of byways; and the objective of arriving at a reasonably honest but concise account of the Itô integral decided most of the material. With motivation from elementary probability we discuss measures and integrals, leading via L2theory and conditional expectation to discrete martingales and an outline proof of the RadonNikodym Theorem. The last two chapters introduce Brownian Motion and Itô integrals, with a brief look at martingale calculus. Here proofs of several key results are only sketched briefly or omitted. The BlackScholes option pricing model provides the main application. None of the results presented is new; any remaining errors are mine" Provided by publisher.
 Supplemental links
 Cover image
Subjects
 Subject
 Measure theory > Textbooks.
Bibliographic information
 Publication date
 2011
 Responsibility
 Ekkehard Kopp.
 Series
 African Institute of Mathematics Library Series
 ISBN
 9781107400863
 1107400864