Overview

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 FAllmer, 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.

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9786610724918

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From the reviews: <p> It serves as an introduction to stochastic calculus and integration without any measure theoretical background a ] . In summary the book provides a very readable introduction to mathematical finance. a ] For a general mathematician it gives a quick insight into the basic concepts of stochastic analysis and mathematical finance and might give some motivation to study the underlying theory in more detail. (Ludger Overbeck, Mathematical Reviews, Issue, 2007 k)

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