Stochastic Calculus and Financial Applications / Edition 1

Stochastic Calculus and Financial Applications / Edition 1

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by J. Michael Steele
     
 

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ISBN-10: 1441928626

ISBN-13: 9781441928627

Pub. Date: 12/01/2010

Publisher: Springer New York

Shastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas.

From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the

Overview

Shastic calculus has important applications to mathematical finance. This book will appeal to practitioners and students who want an elementary introduction to these areas.

From the reviews: "As the preface says, ‘This is a text with an attitude, and it is designed to reflect, wherever possible and appropriate, a prejudice for the concrete over the abstract’. This is also reflected in the style of writing which is unusually lively for a mathematics book." —ZENTRALBLATT MATH

Product Details

ISBN-13:
9781441928627
Publisher:
Springer New York
Publication date:
12/01/2010
Series:
Stochastic Modelling and Applied Probability Series, #45
Edition description:
Softcover reprint of hardcover 1st ed. 2001
Pages:
302
Product dimensions:
0.65(w) x 9.21(h) x 6.14(d)

Table of Contents

Random Walk and First Step Analysis
• First Martingale Steps
• Brownian Motion
• Martingale—Next Steps
• Richness of Paths
• Itô Integration
• Localization and Itô's Integral
• Itô's Formula
• Shastic Differential Equations
• Arbitrage and SDE's
• The Diffusion Equation
• Representation Theorems
• Girsanov Theory
• Arbitrage and Martingales
• The Feynman-Kac Connection

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Stochastic Calculus and Financial Applications 5 out of 5 based on 0 ratings. 1 reviews.
Guest More than 1 year ago
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.