Product Description

Modelling with the Itô integral or stochastic differential equations has become increasingly important in various applied fields, including physics, biology, chemistry and finance. However, stochastic calculus is based on a deep mathematical theory.

This book is suitable for the reader without a deep mathematical background. It gives an elementary introduction to that area of probability theory, without burdening the reader with a great deal of measure theory. Applications are taken from stochastic finance. In particular, the Black Scholes option pricing formula is derived. The book can serve as a text for a course on stochastic calculus for non-mathematicians or as elementary reading material for anyone who wants to learn about Itô calculus and/or stochastic finance.

Contents: Preliminaries: Basic Concepts from Probability Theory; Stochastic Processes; Brownian Motion; Conditional Expectation; Martingales; The Stochastic Integral: The Riemann and Riemann Stieltjes Integrals; The Itô Integral; The Itô Lemma; The Stratonovich and Other Integrals; Stochastic Differential Equations: Deterministic Differential Equations; Itô Stochastic Differential Equations; The General Linear Differential Equation; Numerical Solution; Applications of Stochastic Calculus in Finance: The Black Scholes Option-Pricing Formula; A Useful Technique: Change of Measure; Appendices: Modes of Convergence; Inequalities; Non-Differentiability and Unbounded Variation of Brownian Sample Paths; Proof of the Existence of the General Itô Stochastic Integral; The Radon Nikodym Theorem; Proof of the Existence and Uniqueness of the Conditional Expectation.

Product Details

• Amazon Sales Rank: #500992 in Books
• Published on: 1999-10-30
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 212 pages

Review
"It can be strongly recommended to graduate students and practitioners in the field of finace and economics." -- Mathematics Abstracts, 2000

"this is a well-written book, which makes the difficult object of mathematical finance easy to understand also for non-mathematicians." -- Statistical Papers, 2000

Customer Reviews

Perfect bridge to higher financial math
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.

pedagogically exemplary but finance is far from view
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...

Stochastic Calculus for the Rest of Us
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.