This book is an extremely good introduction to the stochastic calculus field. Indeed, it does not go into too much details and hence, if you are not a pure mathematician, you will still be able to get the idea and the key points of the field.
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).
I came across stochastic differential equations in my work. I could simply have taken the rote formulas and scribbled away, but that approach never delivers wholly satisfactory results. When I translate a computation into the very unusual computing fabric in which I deal, I need to step past the last line in the proof. Many paths lead to that endpoint, all of which differ in how the mathematics matches the computing engine. Part of my job lies in mating the approach to a solution with the vehicle in which you approach 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.
First of all, and most importantly, this is a math book with some finance in it, not the other way around, so you need to know some math before tackling it! If you find Newtonian Calculus complicated, Stochastic Calculus (which, in the realm of mathematics, is not the easiest of topics to start with) is not for you.
The aim of the book is not to present mathematical finance theory, such as option pricing or the Black and Scholes framework, etc... but simply to provide a little formalism and a lot of intuition allowing to better understand random processes and how they can be built at the infinitesimal level from Brownian Motion and previsible functions, and the macro properties that follow from there. Yes, random processes are at the heart of structured finance, but the goal of the author is simply to provide the tools necessary to better grasp financial applications... elsewhere. Therefore, Mikosh opted for an intuitive and rather informal approach presented in a mere 200 pages, which is quite refreshing in a field dominated by very technical and formal 500 page snoozers.
Given the scope and objectives of the book, there is no doubt that this is one of the best (and most affordable) reference available to simply and quickly gain an applied understanding of basic Stochastic Calculus. It can be used as an introduction to the topic before tackling more difficult and thorough books on SDE, or simply as a means of getting familiar with the ideas of Stochastic Calculus without bothering too much with the details of the proofs and move on to finance applications.
Being a strong believer that, at first, ideas are more important than the complex intricacies of formal proofs, this book allowed me to quickly gain a sound footing in SDE... Kudos to the author.
This book provides an excellent mild introduction of stochastic calculus and stochastic differential equations to someone like me who do not have a first mathematics degree (haven't done measure theories). Although the final chapter on application to finance is not as good as other financial maths books such as Joshi's Concepts and Baxter&Rennie's Financial Calculus. Overall, this book sets some firm grounds for further studies on stochastic calculus & financial maths. In addition, the price is low for this book with a hardcover.
This book may be fine if you have at least an undergraduate degree in math. I have an engineering degree with a minor in math, have read many books on quantitative finance, read math books and work math problems for furn, have several years' work experience in analyzing and hedging with derivatives, am taking a course in quantitative finance, and have worked many problems in stochastic calculus. I was actually MORE confused AFTER reading this book (I'm not exaggerating). This book should definitely not have "elementary" in the title.
But whatever your level, there are other books that cover the topic much more clearly and comprehensively. Start with Nefti's Intro to the Mathematics of Financial Derivatives; it's the best. Then read Joshi's Concepts and Practices of Mathematical Finance. Then you may be able to understand Steele's Stochastic Calculus and Financial Applications. Steele doesn't pretend to be a book for beginners, but it is actually more comprehensible to beginners than Mikosch's book.
But if you are more comfortable with reams of mathematical notation and do not require much explanation of that notation, Mikosch may be just what you want.
It is amazing that the author can expose the difficult topics step-by-step clearly in such a little book of less than 200 pages. Mikosch starts the book by introducing basic probability theories and stochastic processes which are prerequisite for the development of stochastic integrals, techniques for solving stochastic differential equations and applications in modern finance. However, reader should be aware that although the book is recommended for those without "deep" mathematical background, it is not suitable for average advanced undergraduates and practitioners without serious statistics and advanced claculus trainings. In my opinion, this book is suitable for those whos have finished the book like Financial Calculus by Baxter and Rennie and are looking for more formal details of the subject matter.
Product Details :
Hardcover: 212 pages
Publisher: World Scientific Publishing Company (October 30, 1999)
Language: English
ISBN-10: 9810235437
ISBN-13: 978-9810235437
Product Dimensions: 6.4 x 0.6 x 9.1 inches
More Details about Elementary Stochastic Calculus With Finance in View, Advanced Series on Statistical Science & Applied Probability, Vol 6, Advanced Series on Statistical Science and Applied Probability, 1st edition
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