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The scope of this book is to give an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes. It will also present related mean-reverting processes that take values in the set of correlation matrices. There will be a particular emphasis on simulation methods for these diffusions. These methods are necessary to get a practical use of these processes. We will also present some models in mathematical finance that use these diffusions. Numerical illustrations will be given on some practical examples.
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