Mathematics of Financial Markets
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.
中文| PDF | 2005 | 355页| ISBN:0387212922 | 2 MB这本书针对的是希望了解快速发展的数学背景的读者？数学领域？金融。它的内容特别适合具有测度论和概率论背景的数学研究生。整个过程的重点是在理论应用的背景下发展理论所需的数学概念。没有试图涵盖令人眼花缭乱的各种小说（或“异国情调”）吗？现在出现在衍生品市场上的金融工具；贯穿始终的重点仍然是严格开发更基本的选项，这些选项是鞅理论当前在？金融市场。这个？rst？第五章在离散时间框架内介绍了该理论。不需要随机微积分，任何熟悉基本概率论和线性代数的人都应该可以访问这些材料。第一章介绍了套利定价（或者更确切地说，非套利定价）的基本思想。给出了单期二项式模型中欧式期权的唯一价格，然后将其扩展到多期二项式模型。第二章介绍了价格过程鞅测度的概念。在讨论了自我使用之后？在对冲交易风险的融资策略中，展示了如何使用等价度量对期权进行定价，其中贴现价格p是鞅。本站不对文件进行储存，仅提供文件链接，请自行下载，本站不对文件内容负责，请自行判断文件是否安全，如发现文件有侵权行为，请联系管理员删除。
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