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Hardcover ISBN:  9781470460143 
eBook: ISBN:  9781470465971 
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Hardcover ISBN:  9781470460143 
Product Code:  GSM/214 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470465988 
Product Code:  GSM/214.S 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
eBook ISBN:  9781470465971 
EPUB ISBN:  9781470469375 
Product Code:  GSM/214.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470465988 
eBook ISBN:  9781470465971 
Product Code:  GSM/214.S.B 
List Price:  $170.00 $127.50 
MAA Member Price:  $153.00 $114.75 
AMS Member Price:  $136.00 $102.00 
Hardcover ISBN:  9781470460143 
eBook ISBN:  9781470465971 
Product Code:  GSM/214.B 
List Price:  $210.00 $167.50 
MAA Member Price:  $189.00 $150.75 
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Book DetailsGraduate Studies in MathematicsVolume: 214; 2021; 309 ppMSC: Primary 60; 91; Secondary 46
This book develops a mathematical theory for finance, based on a simple and intuitive absenceofarbitrage principle. This posits that it should not be possible to fund a nontrivial liability, starting with initial capital arbitrarily near zero. The principle is easytotest in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the socalled “Kelly” or growthoptimal portfolio, of the logoptimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization.
The book contains a considerable amount of new research and results, as well as a significant number of exercises. It can be used as a basic text for graduate courses in Probability and Stochastic Analysis, and in Mathematical Finance. No prior familiarity with finance is required, but it is assumed that readers have a good working knowledge of real analysis, measure theory, and of basic probability theory. Familiarity with stochastic analysis is also assumed, as is integration with respect to continuous semimartingales.
ReadershipGraduate students and researchers interested in math finance.

Table of Contents

Chapters

The market

Numéraires and market viability

Financing optimization maximality

Ramifications and extensions

Elements of functional and convex analysis


Additional Material

Reviews

...this book is for you if you are the kind of soul that is not content with 'what' or 'how' but insists on asking 'why.'
Paolo Guasoni, Dublin City University and University of Bologna


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This book develops a mathematical theory for finance, based on a simple and intuitive absenceofarbitrage principle. This posits that it should not be possible to fund a nontrivial liability, starting with initial capital arbitrarily near zero. The principle is easytotest in specific models, as it is described in terms of the underlying market characteristics; it is shown to be equivalent to the existence of the socalled “Kelly” or growthoptimal portfolio, of the logoptimal portfolio, and of appropriate local martingale deflators. The resulting theory is powerful enough to treat in great generality the fundamental questions of hedging, valuation, and portfolio optimization.
The book contains a considerable amount of new research and results, as well as a significant number of exercises. It can be used as a basic text for graduate courses in Probability and Stochastic Analysis, and in Mathematical Finance. No prior familiarity with finance is required, but it is assumed that readers have a good working knowledge of real analysis, measure theory, and of basic probability theory. Familiarity with stochastic analysis is also assumed, as is integration with respect to continuous semimartingales.
Graduate students and researchers interested in math finance.

Chapters

The market

Numéraires and market viability

Financing optimization maximality

Ramifications and extensions

Elements of functional and convex analysis

...this book is for you if you are the kind of soul that is not content with 'what' or 'how' but insists on asking 'why.'
Paolo Guasoni, Dublin City University and University of Bologna