PDE and Martingale Methods in Option Pricing
This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arb
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What good is it for a man to gain the whole world, yet forfeit his life? Mc. 8, 36
Andrea Pascucci
PDE and Martingale Methods in Option Pricing
Andrea Pascucci Department of Mathematics University of Bologna [email protected]
B&SS – Bocconi & Springer Series ISSN print edition: 2039-1471
ISSN electronic edition: 2039-148X
ISBN 978-88-470-1780-1
e-ISBN 978-88-470-1781-8
DOI 10.1007/978-88-470-1781-8
Library of Congress Control Number: 2010929483
Springer Milan Dordrecht Heidelberg London New York © Springer-Verlag Italia 2011
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Preface
This book gives an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. It is intended as a textbook for graduate and advanced undergraduate students, but I hope it will be useful also for researchers and professionals in the financial industry. Stochastic calculus and its applications to the arbitrage pricing of financial derivatives form the main theme. In presenting these, by now classic, topics, the emphasis is put on the more quantitative rather than economic aspects. Being aware that the literature in this field is huge, I mention the following incomplete list of monographs whose contents overlap with those of this text: in alphabetic order, Avellaneda and Laurence [14], Benth [43], Bj¨ ork [47], Dana and Jeanblanc [84], Dewynne, Howison and Wilmott [340], Dothan [100], Duffie [102], Elliott and Kopp [120], Epps [121], Follmer and Schied [134], Glasserman [158], Huang and Litzenberger [171], Ingersoll [178], Karatzas [200; 202], Lamberton and Lapeyre [226], Lipton [239], Merton [252], Musiela and Rutkowski [261], Neftci [264], Shreve [310; 311], Steele [315], Zhu, Wu and Chern [349]. What distinguishes this book from others is the attempt to present the matter by giving equal weight to the probabilistic point of view, based on the martingale the
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