Mathematics of Financial Markets
The text should prove useful to graduates with a sound mathematical background, ideally a knowledge of elementary concepts from measuretheoretic probability, who wish to understand the mathematical models on which the bewildering multitude of current financial instruments used in derivative markets...
Main Authors:  , 

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Format:  eBook 
Language:  English 
Published: 
New York, NY
Springer New York
2005, 2005

Edition:  2nd ed. 2005 
Series:  Springer Finance Textbooks

Subjects:  
Online Access:  
Collection:  Springer eBooks 2005  Collection details see MPG.ReNa 
Summary:  The text should prove useful to graduates with a sound mathematical background, ideally a knowledge of elementary concepts from measuretheoretic probability, who wish to understand the mathematical models on which the bewildering multitude of current financial instruments used in derivative markets and credit institutions is based. The first edition has been used successfully in a wide range of Master’s programs in mathematical finance and this new edition should prove even more popular in this expanding market. It should equally be useful to risk managers and practitioners looking to master the mathematical tools needed for modern pricing and hedging techniques. Robert J. Elliott is RBC Financial Group Professor of Finance at the Haskayne School of Business at the University of Calgary, having held positions in mathematics at the University of Alberta, Hull, Oxford, Warwick, and Northwestern. He is the author of over 300 research papers and several books, including Stochastic Calculus and Applications, Hidden Markov Models (with Lahkdar Aggoun and John Moore) and, with Lakhdar Aggoun, Measure Theory and Filtering: Theory and Applications. He is an Associate Editor of Mathematical Finance, Stochastics and Stochastics Reports, Stochastic Analysis and Applications and the Canadian Applied Mathematics Quarterly. P. Ekkehard Kopp is Professor of Mathematics, and a former ProViceChancellor, at the University of Hull. He is the author of Martingales and Stochastic Integrals, Analysis and, with Marek Capinski, of Measure, Integral and Probability. He is a member of the Editorial Board of Springer Finance. The new edition adds substantial material from current areas of active research, notably: a new chapter on coherent risk measures, with applications to hedging a complete proof of the first fundamental theorem of asset pricing for general discrete market models the arbitrage interval for incomplete discretetime markets characterization of complete discretetime markets, using extended models risk and return and sensitivity analysis for the BlackScholes model The treatment remains careful and detailed rather than comprehensive, with a clear focus on options. From here the reader can progress to the current research literature and the use of similar methods for more exotic financial instruments. This book presents the mathematics that underpins pricing models for derivative securities, such as options, futures and swaps, in modern financial markets. The idealized continuoustime models built upon the famous BlackScholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discretetime framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuoustime theory, which includes a detailed analysis of the BlackScholes model and its generalizations, American put options, term structure models and consumptioninvestment problems. The mathematics of martingales and stochastic calculus is developed where it is needed. 

Physical Description:  XII, 354 p online resource 
ISBN:  9780387226408 