Peacocks and Associated Martingales, with Explicit Constructions

• Κύριοι συγγραφείς: Hirsch, Francis (Συγγραφέας), Profeta, Christophe (Συγγραφέας), Roynette, Bernard (Συγγραφέας), Yor, Marc (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Milano : Springer Milan, 2011.
• Σειρά: B&SS — Bocconi & Springer Series,
• Θέματα: Mathematics.; Economics, Mathematical.; Probabilities.; Probability Theory and Stochastic Processes.; Quantitative Finance.
• Φυσική περιγραφή: XXXII, 388 p. online resource.
• ISBN: 9788847019089
• ISSN: 2039-1471

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.