A graduate-course text, written for readers familiar with measure-theoretic probability and discrete-time processes, wishing to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed, illustrated by results concerning representations of martingales and change of measure on Wiener space, which in turn permit a presentation of recent advances in financial economics. The book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The whole is backed by a large number of problems and exercises.
这书写作上有些问题。读前两章时根本不知道作者要干什么,直到读到第三章,才发现原来这是一本关于鞅论的书。读到四五章才明白前面忙活半天是为了什么。到最后一章又不明白作者要干什么了。 这完全是本反方向的书,既不从特殊到一般,又不从应用引出理论。上来就直接对鞅对局部...
评分这书写作上有些问题。读前两章时根本不知道作者要干什么,直到读到第三章,才发现原来这是一本关于鞅论的书。读到四五章才明白前面忙活半天是为了什么。到最后一章又不明白作者要干什么了。 这完全是本反方向的书,既不从特殊到一般,又不从应用引出理论。上来就直接对鞅对局部...
评分不及Shreve的那两本清晰,当然也是因为研究生教材更难一些
评分What the hell is this?! What the hell is that?!
评分题暂时没时间刷了。做Diffusion的我觉得都需要至少过一遍这本书。
评分题暂时没时间刷了。做Diffusion的我觉得都需要至少过一遍这本书。
评分基本的金融数学(随机微积分)参考书
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