Elementary Stochastic Calculus With Finance in View (Advanced Series on Statistical Science & Applied Probability, Vol 6) |  | Author: Thomas Mikosch
Publisher: World Scientific Publishing Company
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Rating:  15 reviews
Sales Rank: 266500
Media: Hardcover
Pages: 212
Number Of Items: 1
Shipping Weight (lbs): 1.1
Dimensions (in): 8.6 x 6.2 x 0.5
ISBN: 9810235437
Dewey Decimal Number: 519.2
EAN: 9789810235437
ASIN: 9810235437
Publication Date: October 30, 1999
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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.
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| Customer Reviews:
Showing reviews 1-5 of 15
 Excellent introduction to stochastic calculus June 13, 2008
Viviana Fernandez (Santiago, Chile)
I found this textbook extremely teaching-oriented and an excellent introduction to a very hard subject, such as stochastic calculus. I would definitely recommend it for a Master's level financial engineering course.
 Demanding, but potentially rewarding March 27, 2008
wiredweird (Earth, or somewhere nearby)
2 out of 5 found this review helpful
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.
-- wiredweird
Not a finance book, but one hell of an applied math book... October 16, 2007
Michel Trudelle
4 out of 4 found this review helpful
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...
Great Introduction September 1, 2007
C. Yang (Shanghai, CHN)
1 out of 1 found this review helpful
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.
 Not for beginners or intermediates March 3, 2007
Polymath-In-Training (Olive Branch, MS United States)
10 out of 16 found this review helpful
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.
Showing reviews 1-5 of 15
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