Peacocks and Associated Martingales, with Explicit Constructions
| Autor: | Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor |
|---|---|
| EAN: | 9788847019089 |
| eBook Format: | |
| Sprache: | Englisch |
| Produktart: | eBook |
| Veröffentlichungsdatum: | 24.05.2011 |
| Kategorie: | |
| Schlagworte: | Brownian motion Convex order Markov processes Martingales Peacocks |
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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.
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