Elementary Stochastic Calculus With Finance in View

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Summary: Stochastic Calculus for the Rest of Us
Review: I have recently started to work with stochastic calculus. While I do have a mathematical background and I do understand advanced concepts like measure theory, I wanted something that I could bring down to a level that I could see the wood from the trees. This is pedagogically better.
Unfortunately, there are so few books out there that strive to be anything but a way to demonstrate the author's cleverness that when I do find a book that is understandable by someone who has had no training in that field, I can't sing its praises enough (For physics people Feyman's lectures are easily the best).
Mikosch explains things in a clear easily understandable way. He goes over probability theory, stochastic processes, the Ito Integral and all the basic ideas. While the book is not necessarily rigourous, someone starting is probably more interested in understanding the concepts and saving the rigour for later.
Understanding the core concepts now allows me to read other textbooks in more detail and it even lets me play with the concepts.
For starting quants, this book rocks.

Rating:
Summary: Perfect bridge to higher financial math
Review: Not having a strong theoretical mathematics background hindered my ability to read advanced stochastic finance. I found most "introduction to financial mathematics" for derivatives either too elementary or too advanced (i.e. unreadable). Mikosch has done an outstanding job of explaining key concepts of stochastic calculus, without losing a mathematically unsophisticated reader. After reading this book, one should feel comfortable reading more advanced texts on derivatives, which are usally full of mathematical jargon. I think, it's more suitable for readers with economics or engineering backgrounds who want to further explore the world of financial derivatives. If you have strong background in Analysis and Measure Theory, you might find this book too slow and not detailed enough (but then you are not the intended audience). Also, the book in itself is just an entry point into stochastic calculus and you'll need more advanced/theoretical texts on derivatives after. In my opinion, the book is not suitable for people who just want preliminary knowledge of derivatives; they should look for broader finance books, which usually have a few chapters on derivatives.

Rating:
Summary: Good Cover 2 Cover
Review: This book certainly arouses the interest of the professional as well as the student. Its range is fascinating and it goes behind the standard textbook format to the underlying concepts which aid in understanding an otherwise forbidding subject. The linkage with finance and stocks aids integration with daily happenings . This link in my opinion is very vital for serious practitioners of the science of probabili5ty which has been hitherto shrouded in mystery. I wish all the readers happy times and commend the author and publishers for bringing out a well thought out book which is very user friendly. venkkat

Rating:
Summary: pedagogically exemplary but finance is far from view
Review: This book might just be the first ideal reading that students having to struggle with more advanced texts should do. The level is truly elementary and can be understood with the minimal 1-year college background, which is quite a feat compared with other books with similar claims. Examples are abundant and complement the pedagogically brilliant exposition by making everything intuititive. The style and level is reminiscent of Sheldon Ross' classics in probability and stochastic processes. However, even though advanced topics such as Paley-Wiener representation, Stratonovitch integral and numerical integration schemes are (alas too briefly) covered, the section about finance is disappointing and way too short. In summary an excellent book but look somewhere else for finance applications. And beg Prof. Mikosch for doubling the number of pages in the next edition...

Rating:
Summary: Excellent first introduction
Review: This is the most readable, and technical, introduction to stochastic calculus that I'm aware of. It doesn't really matter that finance is far from you. You can learn all the finance that you want, at an equally pedagogical level from Bjork's book, to give an example, as soon as you finish this. The only thing I miss in this book are equally pedagogical exercises + worked solutions. I hope that the next edition will be twice as large.