Rating: 
Summary: Riskfree profit !!
Review: The book is at the interface of three areas, math, statistics, and finance. While connections between the first two have a long history, it was the connection to finance that caught my attention. Coming from math myself, I needed first to take a closer look at the book to orient myself. The mathematical subjects, smooth sailing, include stochastic differential equations (SDE) as they relate to PDEs; and the ideas from probability and statistics include Brownian motion, martingales, stochastic processes, and the Feynman-Kac connection. Browsing the chapters I found them to be a lovely presentation of ideas with which I am familiar. For me, it was chapter 10 that turned out to have stuff that I wasn't familiar with. That is the finance part, and it is based on a model for Option Pricing developed in 1973 by Fischer Black and Myron Scholes. An arbitrage opportunity [simplified] amounts to the simultaneous purchase and sale of related securities which is guaranteed to produce a *riskless* profit. It was after reading more in this chapter I understood why the book is used in a course at the Wharton School at the University of Pennsylvania. I am impressed with the level of math in this course. Part of the motivation in the applications to finance is that arbitrage enforces the price of most derivative securities. And I learned from ch 10 that the SDE of the Black-Scholes model governs the processes which represent the two variables S, the price of a stock, and B the price of a bond, both S and B representing stochastic variables depending of time t, i.e., both stochastic processes. In the model, S is a geometric Brownian motion, and B is a deterministic process with exponential growth. The two are determined as solutions to the SDE of Black-Scholes.
Rating: 
Summary: I Hate It When Books Lie About Mathematical Requriements
Review: The book says that its only prerequisites are calculus and probability. This is not true. To be able to understand everything that's going on, you'll need to have a very good grasp of subjects like measure-theoretic probability, Hilbert spaces, and functional analysis. I quit reading the book in the early chapters, when Steele starts talking about things like "spans" and "denseness" for function spaces. I don't know where you went to school, but at my school, I didn't learn these subjects in my intro calculus and probability classes. To summarize, don't buy this book if you don't know measure theory.If you want to learn quant finance at an elementary level, Baxter and Rennie is much, much better. Moreover, if you're comfortable with measure theory,and you want to learn the math that's necessary for option pricing, you'd be better off buying Oksendal's excellent book, which is at least as rigorous as Steele's book but much more clear.
Rating: 
Summary: Good Introduction To A Difficult Subject
Review: The goal of this book is to disseminate the knowledge of a very technical subject to a very wide range of audience, including finance professionals. The author did a respectable job in that regard. With some improvement in future revisions, this book seems to be one of the best introductionary texts on stochastic calculus.
Rating:
Summary: Stochastic Calculus and Financial Applications (Applications
Review: This is a really lucid and detailed introduction to derivative pricing theory from the pde way of doing things. The author is an applied mathematician, of the fluid mechanics variety, and this should tell you right away what the drift of the presentation is like.
Rating:
Summary: The book I wish I had 5 years ago!
Review: Written in an unassuming and humorous style with practical examples and interesting excercises. If you want to learn Stochastic Calculus without forgetting why you wanted to learn it, this is the book. After wading through the books by Durrett, Oksendal and Revuz & Yor, I can say with confidence that for those whose first interest is finance, but who want to actually use Stochastic Calculus, this is the place to start. That is not to say that it is light on the mathematics side, but where possible the financial applications drive the discourse. From a mathematical standpoint, this book covers much of the same material as the delightful "Probability With Martingales", by David Williams. From among finance books I am familiar with, "Financial Calculus : An Introduction to Derivative Pricing" by Rennie & Baxter takes a similar, but less mathematical approach, however I find the explanations in this book more transparent and the excercises more relevant--In the end you will know much more about Stochastic Calculus if you choose Steele.
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