Peacocks and Associated Martingales, with Explicit Constructions [electronic resource] / by Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor.
By: Hirsch, Francis [author.].
Contributor(s): Profeta, Christophe [author.] | Roynette, Bernard [author.] | Yor, Marc [author.] | SpringerLink (Online service).
Material type:
BookSeries: B&SS — Bocconi & Springer Series: Publisher: Milano : Springer Milan, 2011Description: XXXII, 388 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9788847019089.Subject(s): Mathematics | Finance | Distribution (Probability theory) | Mathematics | Probability Theory and Stochastic Processes | Quantitative FinanceDDC classification: 519.2 Online resources: Click here to access online Some Examples of Peacocks -- The Sheet Method -- The Time Reversal Method -- The Time Inversion Method -- The Sato Process Method -- The Stochastic Differential Equation Method -- The Skorokhod Embedding (SE) Method. Comparison of Multidimensional Marginals.
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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