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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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VII.9 The Mathematics of Money

Mark Joshi

1 Introduction

The last twenty years have seen an explosive growth in the use of mathematics in finance. Mathematics has made its way into finance mainly via the application of two principles from economics: market efficiency and no arbitrage.

Market efficiency is the idea that the financial markets price every asset correctly. There is no sense in which a share can be a “good buy,” because the market has already taken all available information into account. Instead, the only way that we have of distinguishing between two assets is their differing risk characteristics. For example, a technology share might offer a high rate of growth but also a high probability of losing a lot of money, while a U.K. ...

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