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Mathematics of Financial Markets
Robert J. ElliottP. Ekkehard Kopp
出版Springer Science & Business Media, 2005
主題Business & Economics / GeneralBusiness & Economics / Accounting / GeneralBusiness & Economics / Finance / GeneralBusiness & Economics / Investments & Securities / GeneralBusiness & Economics / Investments & Securities / OptionsBusiness & Economics / Investments & Securities / Analysis & Trading StrategiesBusiness & Economics / StatisticsBusiness & Economics / Business MathematicsMathematics / GeneralMathematics / AppliedMathematics / CalculusMathematics / Game TheoryMathematics / Probability & Statistics / GeneralMathematics / Probability & Statistics / Stochastic ProcessesMathematics / Mathematical Analysis
ISBN03872129229780387212920
URLhttp://books.google.com.hk/books?id=A7AogNCBew8C&hl=&source=gbs_api
EBookSAMPLE
註釋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.