Methods of Mathematical Finance
This monograph is a sequel to Brownian Motion and Stochastic Calculus by the same authors. Within the context of Brownian-motion-driven asset prices, it develops contingent claim pricing and optimal consumption/investment in both complete and incomplete m
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Ioannis Karatzas Steven Shreve
Methods of Mathematical Finance
Probability Theory and Stochastic Modelling Volume 39
Editors-in-Chief Søren Asmussen, Aarhus, Denmark Peter W. Glynn, Stanford, USA Thomas G. Kurtz, Madison, WI, USA Yves Le Jan, Orsay, France Advisory Board Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Andreas E. Kyprianou, Bath, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, BC, Canada Halil Mete Soner, Zürich, Switzerland
The Probability Theory and Stochastic Modelling series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
Gaussian processes Markov processes Random fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, including simulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochastic processes • Stochastic control • Stochastic models in operations research and stochastic optimization • Stochastic models in the physical sciences
More information about this series at http://www.springer.com/series/13205
Ioannis Karatzas • Steven E. Shreve
Methods of Mathematical Finance
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Ioannis Karatzas Departments of Mathematics and Statistics Columbia University New York, NY 10027 USA
Steven E. Shreve Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213 USA
Mathematics Subject Classification (1991): 90A09, 60G44, 93E20 Library of Congress Cataloging-in-Publication Data Karatzas, Ioannis. Methods of mathematical finance / Ioannis Karatzas, Steven E. Shreve. p. cm.—(Applications of mathematics; 39) Includes bibliographical references and index. ISBN 978-1-4939-6814-5 1. Business mathematics. 2. Finance—Mathematical models. 3. Brownian motion processes. 4. Contingent valuation. I. Shreve, Steven E. II. Title. III. Series HF5691.K3382 1998 650'.01'513—dc21 98-14284 ISSN 2199-3130 Probability Theory and Stochastic Modelling ISBN 978-1-4939-6814-5 (h
