ELEMENTARY STOCHASTIC CALCULUS, WITH FINANCE IN VIEW (Advanced Statistical Science and Applied Probability)

In the span of 200 pages, the author succeeds admirably in balancing the needs of three audiences (at least), (i) math students, (ii) students from neighboring areas (finance, economics, statistics, actuarial science, engineering, and more); and (iii) readers who want a quick intro to the basic ideas of stochastic analysis, and its applications. Bravo!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.

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).

The introduction of the book says that "elementary" and "stochastic calculus" are contradictory terms. So not sure I can attribute it to the author. The language is fluid. I guess author tried his best. But overall, the book is not elementary enough. At least not elementary for me. Almost 2 weeks I am struggling, I am still stuck in chapter 1. The chapter 1 is a shock. I am not a mathematician. I did went through a math minor in my undergrad 30 years ago, so cannot say I remember. However I do have idea of the basic probability theory, but what I feel that to go pass chapter 1 you need to have a complete Stat minor (or may be major) undergrad course under your belt and absolutely fresh in memory. Just having a knowledge of basic probability theory is not enough. I am utterly lost in the mathematical notations of chapter 1.I needed a book to understand Stochastic calculus enough to complete a Certificate Course in Quantitative Finance. I need to understand the stochastic calculus for applications, not a full rigorous "with all proof" theories (but definitely like to get a dumbed down version of them). This book (as some review suggested) may have some finance application example at the end but I now have serious doubt if I can ever go past chapter 1.If anybody reading this review, knows any book which can really deliver stochastic calculus at non mathematics level, please post.I am now scared to try any other book. I am not decided yet if I shall return this book. May be I shall try to go thru chapter 2 without going through the rest of the chapter 1.The language is lucid. It tells me that the author tried his best to explain. So for anybody still have full memory of undergrad stat, this book will be great. It is just not for people like me.

Read this small book before reading Shreve's volume II book.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.

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.