Books are written for use, and the best compliment that the community in the field could have paid to the first edition of 1998 was to buy out the print run, and that of the corrected printing, as happened. Meanwhile, the fastdeveloping field of mathematical finance had moved on, as had our thinking, and it seemed better to recognize this and undertake a thorough-going rewrite for the second edition than to tinker with the existing text.

The second edition is substantially longer than the first; the principal changes are as follows. There is a new chapter (the last, Chapter 9) on credit risk - a field that seemed too important to exclude. We have included continuous-time processes more general than the Gaussian processes of the Black-Scholes theory, in order in particular to model driving noise with jumps. Thus we include material on infinite divisibility and Levy processes, with hyperbolic models as a principal special case, in recognition of the growing importance of 'Levy finance'. Chapter 5 is accordingly extended, and new material on Levy-based models is included in Chapter 7 on incomplete markets. Also on incomplete markets, we include more material on criteria for selecting one equivalent martingale measure from many, and on utility-based approaches. However, arbitrage-based arguments and risk-neutral valuation remain the basic theme.

书籍是为使用而写的，而这一领域的社会本可以对1998年第一版给予最好的赞美，就是买下印刷品的发行量和更正后的印刷品。与此同时，快速发展的数学金融领域也在前进，正如我们的想法一样，认识到这一点并对第二版进行彻底的重写似乎比修改现有的文本要好。

第二版比第一版长得多；主要变化如下。有一个关于信用风险的新章节（最后一章，第9章）——这一领域似乎太重要了，不能排除在外。我们包含了比Black-Scholes理论中的高斯过程更一般的连续时间过程，特别是为了模拟带有跳跃的驱动噪声。因此，我们包括无限可分性和Levy过程的材料，并以双曲模型作为主要特例，以认识到“Levy金融”的日益重要。第5章相应地被扩展，第7章关于不完全市场的新材料包括在基于征税的模型上。同样在不完全市场上，我们包括更多关于从许多中选择一个等价鞅测度的标准，以及基于效用的方法。然而，基于套利的论据和风险中性估值仍是基本主题。