Lecture 10: Change of Measure and the Girsanov Theorem
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چکیده
The Cameron-Martin theorem, which has figured prominently in the developments of the last several lectures, is the most important special case of the far more general Girsanov theorem, which is our next topic of discussion. Like the Cameron-Martin theorem, the Girsanov theorem relates the Wiener measure P to different probability measures Q on the space of continuous paths by giving an explicit formula for the likelihood ratios between them. But whereas the Cameron-Martin theorem deals only with very special probability measures, namely those under which paths are distributed as Brownian motion with (constant) drift, the Girsanov theorem applies to nearly all probability measures Q such that P and Q are mutually absolutely continuous.
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Lecture 4 : Risk Neutral Pricing 1 Part I : The Girsanov Theorem 1 . 1 Change of Measure
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