Peacocks and Associated Martingales, with Explicit Constructions
Author | : Francis Hirsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 412 |
Release | : 2011-05-24 |
ISBN-10 | : 9788847019089 |
ISBN-13 | : 8847019087 |
Rating | : 4/5 (087 Downloads) |
Download or read book Peacocks and Associated Martingales, with Explicit Constructions written by Francis Hirsch and published by Springer Science & Business Media. This book was released on 2011-05-24 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: We call peacock an integrable process which is increasing in the convex order; such a notion plays an important role in Mathematical Finance. A deep theorem due to Kellerer states that a process is a peacock if and only if it has the same one-dimensional marginals as a martingale. Such a martingale is then said to be associated to this peacock. In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings. They are developed in eight chapters, with about a hundred of exercises.