Introduction to Stochastic Calculus for Finance A New Didactic Approach

The large number of already available textbooks on stochastic calculus with specific applications to finance requires a justification for another contribution to this subject. The justifcation is mainly pedagogical. These lecture notes start with an elementary approach to stochastic calculus due to...

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Bibliographic Details
Main Author: Sondermann, Dieter
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2006, 2006
Edition:1st ed. 2006
Series:Lecture Notes in Economics and Mathematical Systems
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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505 0 |a Preliminaries -- to Itô-Calculus -- The Girsanov Transformation -- Application to Financial Economics -- Term Structure Models -- Why Do We Need Itô-Calculus in Finance? -- Appendix: Itô Calculus Without Probabilities 
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520 |a The large number of already available textbooks on stochastic calculus with specific applications to finance requires a justification for another contribution to this subject. The justifcation is mainly pedagogical. These lecture notes start with an elementary approach to stochastic calculus due to Föllmer, who showed that one can develop Ito's calculus "pathwise" as an exercise in real analysis. The text opens to students interested in finance a quick (but by no means "dirty") road to the tools required for advanced finance in continuous time, including option pricing by martingale methods, term structure models in a HJM-framework and the Libor market model. The reader is supposed only to be familiar with elementary real analysis (e.g. Taylor's Theorem) and basic probability theory. The text is also useful for mathematicians interested in the methods of modern mathematical finance without prior knowledge of advanced stochastic analysis