Stochastic Calculus and Financial Applications

Book Description

The Wharton School course on which the book is based is designed for energetic students who have had some experience with probability and statistics, but who have not had advanced courses in stochastic processes. Even though the course assumes only a modest background, it moves quickly and - in the end - students can expect to have the tools that are deep enough and rich enough to be relied upon throughout their professional careers. The course begins with simple random walk and the analysis of gambling games. This material is used to motivate the theory of martingales, and, after reaching a decent level of confidence with discrete processes, the course takes up the more demanding development of continuous time stochastic process, especially Brownian motion. The construction of Brownian motion is given in detail, and enough material on the subtle properties of Brownian paths is developed so that the student should sense of when intuition can be trusted and when it cannot. The course then takes up the It¿ integral and aims to provide a development that is honest and complete without being pedantic. With the It¿ integral in hand, the course focuses more on models. Stochastic processes of importance in Finance and Economics are developed in concert with the tools of stochastic calculus that are needed in order to solve problems of practical importance. The financial notion of replication is developed, and the Black-Scholes PDE is derived by three different methods. The course then introduces enough of the theory of the diffusion equation to be able to solve the Black-Scholes PDE and prove the uniqueness of the solution.

Customer Reviews:

A Beautiful MATH Book.......2006-06-21

Before I write this review, it's only fair to disclose that before even hearing of it I already had a very solid background in (graduate-level) analysis, which as another reader astutely pointed out is often considered "calculus" in the math community (I think the classic Calculus by Shlomo Steinberg, which can be found free online, has been used at Harvard for decades, while Tom Apostol's "Calculus," a misnomer to say the least, is the standard text at Stanford and Cal Tech - both are really books on advanced calculus and elementary real analysis). Part of the reason I am writing this is to clarify the distinction - many people aspiring towards quantitative roles on Wall Street don't know exactly what the mathematical prerequisites are for a particular subject or presentation, and hopefully I can help clarify this for other readers who, like myself, sought books like this one to learn the basics of mathematical finance.

On that note, Steele's book is a MATH book. By contrast, the wonderful book by Baxter & Rennie emphasizes core ideas with emphasis on the relationship between the three primary tools of the discipline (Martingale Representation, Ito-Doeblin Calculus, and the Feynman-Kac formula) while Shreve's classic emphasizes actual development of key models and techniques. Even Oksendal, which is aimed at a slightly more sophisticated mathematical audience, emphasizes applications at the expense of elegance.

In contrast, Steele's book is a math book aimed at Wharton (read: finance and economics doctoral students, likely in their second year) students with varied interests. Students taking this course probably have already taken a rigorous course in asset pricing theory from the academic viewpoint and need to fill in the blanks with the continuous-time techniques to extend these techniques and to understand stochastic calculus at the level necessary for research in economics/finance.

With that in mind, the book is versatile enough to be appreciated by different audiences. Steele certainly takes care give a clear, well-motivated presentation which explains to the reader WHY he is giving a concept, proof, or problem, and breaks the book up into small, digestible chapters. The problems are neither overly difficult nor disconnected from the text, although doing them is not an essential part of understanding the overall view. Furthermore, Steele clearly takes delight in the beauty of stochastic calculus, as demonstrated by Chapter 5 - Richness of Paths, which discusses the "interesting" properties of Brownian motion. For anyone who sat through a difficult analysis class thinking the whole purpose of the course was to annoy and taunt the student with irrelevant counterexamples (remember constructing a continuous yet non-differentiable function using limits?), this chapter will be especially fun.

In the first part of the book, Steele covers the basics of the random walk and martingales, introducing important theorems such as the upcrossing (downcrossing) lemma, submartingales and the Doob Decomposition theorem, the basic martingale inequalities, stopping times, and conditional probability (for those who are familiar with Williams' Probability with Martingales, the treatment is similiar). He then covers Brownian motion from both the standard perspective (a Brownian motion is a process such that...) and more intuitively as a limit of random walks (i.e. the "wavelet" construction/proof), using this subject as an opportunity to extend the martingale concepts to continuous-time.

In what could roughly be called the "second" part of the book, Steele develops the Ito integral as a martingale and as a process. Steele provides a lot of detail to the subject, perhaps in mind with the view that readers using stochastic calculus with more general underlying processes will have to understand the difference between a martingale and "just" a local martingale. He then quickly but sufficiently covers the standard topics of Ito calculus - Ito's lemma, quadratic variation, and the basic SDE, although in the Picard-type existence/uniqueness proof of SDEs he shows why the careful description of the Ito integral is not simply technical.

The next part of the book covers the "standard" topics in financial mathematics that would appeal to quant finance students . The chapter on arbitrage covers the basic Black-Scholes-Merton equation and its generalization to arbitrage pricing, although Steele (appropriately) addresses Black and Scholes CAPM derivation of their options pricing formula, which gives the finance/economics reader a historical perspective. The chapter on diffusions is excellent and gives all of the necessary elements for handling "nice" parabolic second-order equations. He even sneaks in Green's functions, series expansions, and the Maximum Principle without making uninterested readers have to learn them to follow the presentation.

In the last few chapters, he covers Martingale Representation, Girsanov's Theorem and their applications to more advanced topics in pricing, such as forward measures. The problems in this part of the book are nice because they help the reader understand the intuition behind a particular mathematical principle but not necessarily its application to a well-recognized model. The final chapter on the Feynman-Kac formula gives a very intuitive proof of its topic which helps the reader understand what is meant by "killing" a process and hopefully how that translates into finance; other books often just do a coefficient-matching proof, which really doesn't capture what's really going on.

I emphasize again that while the book is designed to serve a different purpose than texts such as Shreve or Baxter & Rennie, it can help readers of different backgrounds understand the basic elements needed for more advanced stochastic analysis and gain an appreciation for both the beauty of the subject and the underlying intuition liking the math to the finance. The prerequisite, though, is at least a (rigorous undergrad) course in real analysis, probably some familiarity with measure theory, probability, and L(p) spaces (or at least L(1,2,inf) spaces), and at least basic familiarity with the elements of stochastic calculus (Ito's lemma and computations with "box calculus", for example). For readers seeking a more comprehensive treatment of quantitative finance, this book is reasonably good mathematical preparation to understand Musiela/Rutkowski, and for doctoral students, understanding most of the topics in this book with a brief introduction to dynamic programming in the continuous-time setting is sufficient background to read Merton's book (consumption-investment problems) as well as understand the basics of derivative pricing.

Good book.......2006-04-23

This is a good start.

One thing about mathematical prerequisitives and a pet peeve.
In general, when mathematicians state that a minimal prerequistive is calculus, they are not refering to the calculus that a science major such as a physicist would study... as David Hilbert once said, Physics is too hard for physicists...this is engineering calculus... this is geared toward usage and application( they are consumers of math). What a mathematician is refering to when they mention calculus is actually analysis...the study of limits, etc. You should be comfortable with topological concepts such as compact sets, open and closed sets, limits, epsilon-delta notation, etc, etc.
So you should keep this in mind. So if you have had a course in classical analysis and a course in probability which makes use of this background, you should have no problem with this book.
But if you are a typical engineer, physicist ( whether PHd or not ) and have never been exposed to the concept of a compact set, or group theory, etc, etc, then you need to do some homework. You will of course have the brain power...you just need the lingo and the concepts...you have probably learned the material but just don't know the math speak for it.
The type of "calculus" book I am thinking of are books such as 'Elementary Classical Analysis' by Jerrold Marsden ( my freshman "calculus" book, or 'Real Analysis' by Royden ( my sophomore "calculus" book ). By all means don't give up...but if you are planning a serious career in quantitative finance, you should master the concepts in these books. They will go a long way to help you master modern economics & finance. This book will too.

I Hate It When Books Lie About Mathematical Requriements.......2003-05-03

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.

Riskfree profit !!.......2003-03-09

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.

Review from a grad student not at Wharton.......2003-01-29

Reading Steele's book without attending has classes at Wharton leaves the reader looking for explanations to equations. Ideas are not clearly explained and problems are not worked out in detail with a descriptive process of how to solve the problem. The brief explanations in this book intended for a reader with knowledge of calculus and probability but not having a background in Stochastic calculus do not provide a sufficient basis for the reader to learn the material.

Book Description

Covers and simplifies every step in the survey process

Measuring the Pulse of the Enterprise Getting the Most from Organizational Surveys

Do you want to bring about change in your organization by measuring its "pulse"—how your people really feel about their work environment?

Are you thinking about conducting a survey, but hesitate because the process is too complicated?

This highly practical guide simplifies the survey process by outlining what needs to be done at every step to get the survey right—and gain full value from this remarkably rich and rewarding experience.

A step-by-step approach that works on any type of survey

Whether you're surveying people's opinions, attitudes, values, beliefs, knowledge, or general views, Measuring the Pulse of the Enterprise will walk you step-by-step through the entire process: Before any widespread survey is conducted, during the information-collection process itself, and after input has been collated and analyzed and it is time to take action.

The book is organized into 15 chapters, each with a one-page summary at the end and recommended resources. Topics covered include:

• Various kinds of surveys and what all must focus on
• How to align a survey with your company's goals
• 3 approaches to designing a survey
• Who should be involved in the design process, how large a population should be surveyed, and how often should a survey be conducted
• Often-overlooked aspects of administering surveys
• Preparing individuals and groups who can help the process enormously—or make it difficult
• How much time each phase of the process should take
• Gathering data in intelligent ways and collating the results efficiently
• Analyzing, documenting, and presenting the results

This manual is packed with information and insights organizations of every size and type will find useful. Whether your survey is a one-time event or part of an ongoing effort to gather employee feedback, Measuring the Pulse of the Enterprise will make the process fast, easy and cost-effective.

Book Description

Reliable methods for monitoring and assessing soil quality are a prerequisite for successful soil bioremediation projects. The fifth volume of Soil Biology presents detailed descriptions of selected methods for evaluating, monitoring and assessing bioremediation treatments of soils contaminated with organic pollutants or heavy metals. Traditional soil investigation techniques, including chemical, physical and microbiological methods, are complemented by the most suitable modern methods, such as the use of bioreporter technology, immunological, ecotoxicological or molecular assays. Feasibility studies for bioremediation treatments complete the manual. Easy-to-follow protocols with step-by-step procedures, lists of the required equipment and reagents as well as notes on the evaluation and quality control allow immediate application. Short introductions to the principles and objectives help to assess the field of application of each procedure.

Book Description

Both regulators and the regulated community can benefit from the thoughtful recommendations presented by experts in whole effluent toxicity (WET) testing and receiving stream impact prediction. This book delivers state-of-the-art assessments that reflect appropriateness of endpoints used in routine WET methods, degree and causes of WET test method variability, biotic and abiotic factors that can influence measured field responses to effluents, and relationships among effluent toxicity, ambient toxicity, and receiving system impacts.

Average customer rating:

A Practical Guide for Beginners

Riviting!!

Good Book For Beginners

Good Sales Tactics

Informative, detailed and more

Denny Brauer's Jig Fishing Secrets
Denny Brauer
Manufacturer: Outdoor World Press
ProductGroup: Book
Binding: Paperback

General | Sports | Subjects | Books
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ASIN: 1879206226

Book Description

Denny Brauer, the acknowledged world renown master of jig fishing reveals his tournament-winning jig fishing secrets in his own, easy-to-read style. Consistently in the money in the professional bass angling circuits, Denny Brauer has won over $1,000,000 on the B.A.S.S. circuit alone. He is also one of the most respected bass anglers in the world and a very popular television personality, seminar speaker and the first bass fisherman to join the ranks of other professional athletes on the Wheaties box.

Customer Reviews:

A Practical Guide for Beginners.......2006-09-04

I recommend this book if you are a jig fishing novice, or don't fish bass jigs, but would like to. If you're a proficient jig fisherman, you probably won't find much new material here. Call it "Jig Fishing 101", if you will.
Brauer takes the reader through proper jig selection, including size, color, skirts, trailers, etc. to match the conditions you're fishing, as well as equipment and techniques, and seasonal adjustments. Understandably, Brauer touts the jig he helped design for Strike King Lures that bears his name. I've used them and they work well. However, other jigs on the market also incorporate many of the design features Brauer deems important, such as a horizontal line tie, sharp needle-point hook, etc.
The thing I like about Denny Brauer is that he speaks to us in simple terms that anyone can understand. He's a good teacher. And most importantly, the man knows what he's talking about. For those who don't already know, Brauer is widely regarded as one of the best jig fisherman in the country. He's made his living doing it, as a professional bass fisherman. Why not learn from one of the best?
Like any other fishing technique, nothing can take the place of time on the water, but once you catch a few fish on a jig, your confidence grows, and like me, you'll have a jig tied on for each fishing trip.
Brauer's book is a worthwhile beginners guide. Hope this review was helpful.

Riviting!!.......2006-03-15

I have read this book cover to cover and found it to be highly informative. One of the things that surprised me that most about this book is the level of insight as to what is going through a jig fisherman's head during a tournament.

Good Book For Beginners.......2004-10-11

The book is an easy read but the information about jig fishing for bass is rather basic. For the novice bass jig fisherman, I think the book would be very helpful. Appropriate tackle such as line, reels and rods are discussed as well seasonal approaches to jig fishing.

Overall, I thought the book lacked in detailed information. The diagrams and maps were quite rudimentary and Denny Brauer talked quite a bit about how his jig by "Strike King" is superior. Plugging his product prevented him from detailing how different jig designs might be a better choice in specific situations.

If you're an advanced bass fisherman, I can't recommend this book but if you're new to using jigs for bass, this book is a good start.

Good Sales Tactics.......2004-02-10

Watch out for the sales tactics. Ask yourself: "Is Strike King's jig that much better than other jigs?". I admit I fell for the sales pitch and ran out and bought the Strike King jigs that Denny mentions throughout the book but don't get sucked in like I did. I'm sure there's alternative jigs on sale that would work out just as good.

Informative, detailed and more.......2001-08-27

Newcomers to jig fishing are going to learn a lot as well as the experienced angler. This book takes you all the way step by step. The book primarily relates to fliping and pitching, focusing on largemouth fishing. Tournament experiences are used to illustrate details of techniques and conditions on how to apply the jig for it's best potential. The stories and experiences are entertaining as well. This book should be a pleasure to read by any angler.

Book Description

Career opportunities for Nursing Assistants are growing every year, but it is extremely difficult to become part of this dynamic workforce. Candidates must pass a tough certification exam and meet employment requirements. This book is the best choice to prepare for the test and for a career as a Nursing Assistant. It offers four complete Nursing Assistant Exams, with full answer explanations and gives a list of resources for job placement services and professional organizations.

Customer Reviews:

nursing assistance/nurse aide exam (second edition).......2006-10-29

I ordered two books at the same time needed both,got one book and the other I waited for weeks and e-mailed xxx3.Amazon does not have the book any more,don't sell this book.Not in stock and can not get it.If I would of know I would not have ordered the other book.P.S. when ordering better make sure they have the book,they'll show the book but they might not have it any more.I'm very disapointed.

Great book for testing knowledge.......2006-07-25

I used this book to study for my CNA exam. As an EMT-B from the Air Force, we are able to do a lot more than a CNA. In studying for this test, this book allowed me to understand and study for my CNA successfully. I had this book in addition to another one on skills. I aced my test thanks to this book!! I think this book was essential in helping me pass my test.

For someone who hasn't taken a CNA course and wants to "challenge the board" to get their CNA, this book is for you.

Very Helpful.......2005-08-08

I used the book to help me prepare for a CNA test. After a three year period of not doing anything with my cna licence this book really recalled all memory. I did great in the test and really aenjoy the job that it helped me get.

Test guide.......2005-07-19

This is a great book for practice tests, but it is not really a study guide. It is still very beneficial in assisting you with testing your knowledge of the material.

Nursing Assistant Exam: The Complete Preparation Guide (Learning Express)

Average customer rating:

AWESOME

Nursing Assistant Exam: The Complete Preparation Guide (Learning Express)

Manufacturer: Learning Express
ProductGroup: Book
Binding: Paperback

General | Test Prep Central | Reference | Subjects | Books

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Issues, Trends & Roles | Nursing | Medicine | Subjects | Books

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ASIN: 1576850536

Book Description

Job prospects for Nursing Assistants are bright. But you need to be fully prepared to pass the necessary certification exams and meet employment requirements. That's why LearningExpress has created this one-of-a-kind guide to make it easier for you every step of the way, from fulfilling the requirements in your area to passing critical written and practical skills exams.

Only LearningExpress gives you All these advantages:
-- Test preparation for the Nursing Assistant Exam National Standards for Certified Nursing Assistants.
-- Four complete Nursing Assistant practice exams, with score-it-yourself answers and full explanations.
-- A customized study plan to help you pinpoint and strengthen areas in which you are weakest.
-- A sample Nursing Assistant Practical Skills Exam.

Plus Exclusive EasySmart Test Prep System to help you:

Develop proven-successful test strategies from professional test-makers -- draw up (and stick to) a study plan that works for you -- get into top shape (physical and mental) for exam day -- overcome test anxiety and mid-test panic -- learn the secrets of guessing successfully -- and more!

Customer Reviews:

AWESOME.......1999-07-15

I HAVE BEEN OUT OF THE MEDICAL FIELD FOR ABOUT 7 YEARS, LOOKING TO GET BACK IN..THIS BOOK WITH THE SELF EXAMS IS AWESOME, BY THE TIME I FINISHED THE FINAL EXAM I SCORED A 90 % ..I AM CONFIDENT WHEN I AM READY TO TAKE MY TEST, I WILL PASS WITH FLYING COLORS..I HIGHLY RECOMMEND THIS TO ANYONE LOOKING TO TAKE THE STATE EXAM OR JUST FOR A REFRESHER...

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