Methods of Mathematical Finance (Stochastic Modelling and Applied Probability) - Hardcover

Ioannis Karatzas

Hardcover

ISBN 10: 0387948392 ISBN 13: 9780387948393

Publisher: Springer, 1998

Synopsis

This sequel to Brownian Motion and Stochastic Calculus by the same authors develops contingent claim pricing and optimal consumption/investment in both complete and incomplete markets, within the context of Brownian-motion-driven asset prices. The latter topic is extended to a study of equilibrium, providing conditions for existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the book. This book will be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

About this title

From the Publisher

Written by two of the best-known researchers in mathematical finance, this book will appeal to theorists and practitioners in this very active research area. It includes much material that has not appeared before in book-form. This book is a sequel to their GTM volume. The book closest in level is Musiela/Rutowski. According to Shreve, M/R is 100% applied while K/S has a mix of practical and theoretical resutls. M/R is more comprehensive. K/S concentrates on their research interests and includes more original work.

From the Back Cover

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 markets. The latter topic is extended to a study of equilibrium, providing conditions for the existence and uniqueness of market prices which support trading by several heterogeneous agents. Although much of the incomplete-market material is available in research papers, these topics are treated for the first time in a unified manner. The book contains an extensive set of references and notes describing the field, including topics not treated in the text. 

This monograph should be of interest to researchers wishing to see advanced mathematics applied to finance. The material on optimal consumption and investment, leading to equilibrium, is addressed to the theoretical finance community. The chapters on contingent claim valuation present techniques of practical importance, especially for pricing exotic options.

Also available by Ioannis Karatzas and Steven E. Shreve, Brownian Motion and Stochastic Calculus, Second Edition, Springer-Verlag New York, Inc., 1991, 470 pp., ISBN 0-387- 97655-8. 

Edition details

• Publisher: Springer
• Publication date: 1998
• Language: English
• ISBN 10: 0387948392
• ISBN 13: 9780387948393
• Binding: Hardcover
• Number of pages: 422