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Peacocks and Associated Martingales, with Explicit Constructions (Bocconi & Springer Series)Francis Hirsch (Author), Christophe Profeta (Author), Bernard Roynette (Author), Marc Yor (Author)



Product DescriptionWe 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.

From the Back CoverWe 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.

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Product Details Hardcover: 430 pages Publisher: Springer; 1st Edition. edition (August 3, 2011) Language: English ISBN-10: 8847019079 ISBN-13: 978-8847019072