Mathematics of Financial Markets

Robert J Elliott, P. Ekkehard Kopp (Autoren)

Buch | Softcover

354 Seiten

2010 | Softcover reprint of hardcover 2nd ed. 2005
Springer-Verlag New York Inc.
978-1-4419-1942-7 (ISBN)

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This work is aimed at an audience with a sound mathematical background wishing to learn about the rapidly expanding ?eld of mathematical ?nance. Its content is suitable particularly for graduate students in mathematics who have a background in measure theory and probability. The emphasis throughout is on developing the mathematical concepts required for the theory within the context of their application. No attempt is made to cover the bewildering variety of novel (or ‘exotic’) ?nancial - struments that now appear on the derivatives markets; the focus throu- out remains on a rigorous development of the more basic options that lie at the heart of the remarkable range of current applications of martingale theory to ?nancial markets. The ?rst ?ve chapters present the theory in a discrete-time framework. Stochastic calculus is not required, and this material should be accessible to anyone familiar with elementary probability theory and linear algebra. The basic idea of pricing by arbitrage (or, rather, by non-arbitrage) is presented in Chapter 1. The unique price for a European option in a single-period binomial model is given and then extended to multi-period binomial models. Chapter 2 introduces the idea of a martingale measure for price processes. Following a discussion of the use of self-?nancing tr- ing strategies to hedge against trading risk, it is shown how options can be priced using an equivalent measure for which the discounted price p- cess is a martingale.

Pricing by Arbitrage.- Martingale Measures.- The First Fundamental Theorem.- Complete Markets.- Discrete-time American Options.- Continuous-Time Stochastic Calculus.- Continuous-Time European Options.- The American Put Option.- Bonds and Term Structure.- Consumption-Investment Strategies.- Measures of Risk.

Erscheint lt. Verlag	25.11.2010
Reihe/Serie	Springer Finance
Reihe/Serie	Springer Finance Textbooks
Zusatzinfo	XII, 354 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Wirtschaft ► Allgemeines / Lexika
	Wirtschaft ► Betriebswirtschaft / Management ► Finanzierung
ISBN-10	1-4419-1942-2 / 1441919422
ISBN-13	978-1-4419-1942-7 / 9781441919427
Zustand	Neuware