ELEMENTARY STOCHASTIC CALCULUS, WITH FINANCE IN VIEW (Advanced Statistical Science and Applied Probability) 1st Ed. Edition
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"this is a well-written book, which makes the difficult object of mathematical finance easy to understand also for non-mathematicians." -- Statistical Papers, 2000
- Publisher : World Scientific Publishing Company; 1st Ed. edition (October 30, 1998)
- Language : English
- Hardcover : 226 pages
- ISBN-10 : 9810235437
- ISBN-13 : 978-9810235437
- Item Weight : 15.8 ounces
- Dimensions : 6 x 0.56 x 9 inches
- Best Sellers Rank: #813,347 in Books (See Top 100 in Books)
- Customer Reviews:
Top reviews from the United States
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Now no short book can cover everything, but what the author does so well is presenting main ideas, so readers who need more can get started; ... they will already have developed some instincts for the subject.
This is tricky, as almost all traditional math courses are "deterministic." By this, I mean they cover differential equations, ordinary and PDE, where solutions are functions of the underlying variables. This is based on physics and on the meaning of uniqueness of solutions: some function which satisfies a PDE and initial (or boundary conditions.)
When I teach a first course in the subject, I find that students have a hard time grasping the meaning of solutions to stochastic differential equations: the meaning of sample paths as solutions. The intuition and the basic tools of Ito calculus.
The author's approach is to start with the most important examples, and to explain their meaning, and their uses: Brownian motion, geometric Bm. Later in the book, the Black Scholes and its relevance for pricing of financial derivatives are covered.
This reviewer has found in teaching beginning graduate courses for a mixed audience of students, both math, and applied, see (i) - (ii) above.
I feel it is a great supplement to any course in this or related subjects. Most students should be able to give it at least a first reading in a couple of days. But I recommend reading it many times.
Review by Palle Jorgensen, June 2013.
The sections on conditional expectataions, martingales, and Brownian motion are well written and simple enough to understand. While not packed with finance examples until the last chapter, the author attempts to provide what is needed of the subject matter to successfully complete a first semester course in Stochastic Calculus. Once read, it's a great second reference.
However, if you are really familiar with math and the probability theories, you might want to go for a more hardcore approach to this field.
This book provides clear definitions, clear theorems, the quality of the book itself is very good (rather small, solid pages).
The financial view is especially available in the last chapter though, but it is really not a problem because I think that it is nearly impossible to apply finance to stochastic calculus without having gone through the whole book first (you need the whole theory to apply it).
Mikosch's slender volume has helped me immensely. It carries every sign of technical brilliance. More than once, an off-hand comment or a couple of lines of inequalities turned months of bafflement into moments of clarity - only the finest minds, Heisenberg among them, have done that for me. Somewhat into the critical insights, however, my own weakness blocked my climb toward the pinnacle of this book's conclusions.
I'm not a mathematician. I'm a math user. I can hang with the probability side of this book as far as it goes, but my insight into calculus has suffered several decades of benign neglect. I hold onto the development well past the 3/4 point in this book, but I admit that my grasp loosens. I'm sure I can get more from the later sections, using either low-order approximations or an intensity of approach that competes with other demands on my attention. I'm still working, but I don't believe that I'll take in all of the understanding that Mikosch gives out.
I am quite sure there is more in this slender book than I have extracted. That is not a problem in the book, but a mismatch between its goals and my preparation. It's helped and could help another person more, but leaves this reviewer looking for just a bit that the author assumed I wouldn't need.
Top reviews from other countries
I thoroughly recommend this text for someone like myself, moving into the Quant space but not necessarily with a French degree in stochastic calculus and needing some background info in order to fully appreciate and understand some models used in finance. Enjoy.
PS. This is a great companion for Hull.
Longer books tend to make you forget the interesting bits, this book has distilled everything and what's left is the very important core. Also it's very well written (easy and interesting to follow)