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Hardcover ISBN:  9780821821237 
Product Code:  GSM/31 
List Price:  $99.00 
MAA Member Price:  $89.10 
AMS Member Price:  $79.20 
Sale Price:  $64.35 
eBook ISBN:  9781470420857 
Product Code:  GSM/31.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Sale Price:  $55.25 
Hardcover ISBN:  9780821821237 
eBook ISBN:  9781470420857 
Product Code:  GSM/31.B 
List Price:  $184.00 $141.50 
MAA Member Price:  $165.60 $127.35 
AMS Member Price:  $147.20 $113.20 
Sale Price:  $119.60 $91.98 

Book DetailsGraduate Studies in MathematicsVolume: 31; 2001; 253 ppMSC: Primary 62; 91; 93; Secondary 49; 60
Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills.
The mathematics involved in modern finance springs from the heart of probability and analysis: the Itô calculus, stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality. Indeed, most of purely mathematical topics are treated in extended “excursions” from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a selfcontained and complete introduction to the underlying mathematics.
This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes an applied introduction to the basics of stochastic processes (martingales and Brownian motion) and stochastic calculus. It would also be suitable for a course in continuoustime finance that assumes familiarity with stochastic processes.
The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential.
ReadershipGraduate level and research mathematicians, physicists, financial analysts, and actuarians interested in mathematical finance.

Table of Contents

Chapters

Chapter 1. The meanvariance approach in a oneperiod model

Chapter 2. The continuoustime market model

Chapter 3. Option pricing

Chapter 4. Pricing of exotic options and numerical algorithms

Chapter 5. Optimal portfolios


Additional Material

Reviews

Especially useful for students seeking a lively introduction to Itô calculus.
Short Book Reviews, International Statistical Institute


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Understanding and working with the current models of financial markets requires a sound knowledge of the mathematical tools and ideas from which they are built. Banks and financial houses all over the world recognize this and are avidly recruiting mathematicians, physicists, and other scientists with these skills.
The mathematics involved in modern finance springs from the heart of probability and analysis: the Itô calculus, stochastic control, differential equations, martingales, and so on. The authors give rigorous treatments of these topics, while always keeping the applications in mind. Thus, the way in which the mathematics is developed is governed by the way it will be used, rather than by the goal of optimal generality. Indeed, most of purely mathematical topics are treated in extended “excursions” from the applications into the theory. Thus, with the main topic of financial modelling and optimization in view, the reader also obtains a selfcontained and complete introduction to the underlying mathematics.
This book is specifically designed as a graduate textbook. It could be used for the second part of a course in probability theory, as it includes an applied introduction to the basics of stochastic processes (martingales and Brownian motion) and stochastic calculus. It would also be suitable for a course in continuoustime finance that assumes familiarity with stochastic processes.
The prerequisites are basic probability theory and calculus. Some background in stochastic processes would be useful, but not essential.
Graduate level and research mathematicians, physicists, financial analysts, and actuarians interested in mathematical finance.

Chapters

Chapter 1. The meanvariance approach in a oneperiod model

Chapter 2. The continuoustime market model

Chapter 3. Option pricing

Chapter 4. Pricing of exotic options and numerical algorithms

Chapter 5. Optimal portfolios

Especially useful for students seeking a lively introduction to Itô calculus.
Short Book Reviews, International Statistical Institute