Mathematics of Financial Markets Mathematics of Financial Markets
Springer Finance

Mathematics of Financial Markets

    • $79.99
    • $79.99

Publisher Description

This book presents the mathematics that underpins pricing models for derivative securities, such as options, futures and swaps, in modern financial markets. The idealized continuous-time models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory, which includes a detailed analysis of the Black-Scholes model and its generalizations, American put options, term structure models and consumption-investment problems. The mathematics of martingales and stochastic calculus is developed where it is needed.


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 discrete-time markets


characterization of complete discrete-time markets, using extended models


risk and return and sensitivity analysis for the Black-Scholes 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.


The text should prove useful to graduates with a sound mathematical background, ideally a knowledge of elementary concepts from measure-theoretic 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 Pro-Vice-Chancellor, 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.

GENRE
Science & Nature
RELEASED
2006
March 30
LANGUAGE
EN
English
LENGTH
366
Pages
PUBLISHER
Springer New York
SELLER
Springer Nature B.V.
SIZE
8.5
MB

More Books Like This

Introduction to Stochastic Finance Introduction to Stochastic Finance
2018
Paris-Princeton Lectures on Mathematical Finance 2004 Paris-Princeton Lectures on Mathematical Finance 2004
2007
Convex Duality and Financial Mathematics Convex Duality and Financial Mathematics
2018
Inspired by Finance Inspired by Finance
2013
From Stochastic Calculus to Mathematical Finance From Stochastic Calculus to Mathematical Finance
2007
Mathematical Control Theory and Finance Mathematical Control Theory and Finance
2009

More Books by Robert J. Elliott & P. Ekkehard Kopp

Hidden Markov Models in Finance Hidden Markov Models in Finance
2007
Hidden Markov Models in Finance Hidden Markov Models in Finance
2014
Introduction to Hidden Semi-Markov Models Introduction to Hidden Semi-Markov Models
2018
Stochastic Calculus and Applications Stochastic Calculus and Applications
2015
Binomial Models in Finance Binomial Models in Finance
2006
Advances in Mathematical Finance Advances in Mathematical Finance
2007

Other Books in This Series

Risk and Asset Allocation Risk and Asset Allocation
2007
Financial Modeling, Actuarial Valuation and Solvency in Insurance Financial Modeling, Actuarial Valuation and Solvency in Insurance
2013
Modelling, Pricing, and Hedging Counterparty Credit Exposure Modelling, Pricing, and Hedging Counterparty Credit Exposure
2009
A Course in Derivative Securities A Course in Derivative Securities
2006
Implementing Models in Quantitative Finance: Methods and Cases Implementing Models in Quantitative Finance: Methods and Cases
2007
Option Prices as Probabilities Option Prices as Probabilities
2010