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Peacocks and Associated Martingales, with Explicit Constructions

by Hirsch, Francis.
Authors: Profeta, Christophe.%author. | Roynette, Bernard.%author. | Yor, Marc.%author. | SpringerLink (Online service) Series: B&SS — Bocconi & Springer Series, 2039-1471 Physical details: XXXII, 388 p. online resource. ISBN: 8847019087 Subject(s): Mathematics. | Finance. | Distribution (Probability theory). | Mathematics. | Probability Theory and Stochastic Processes. | Quantitative Finance.
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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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