Title: Peacocks and associated martingales, with explicit constructions /
Authors: Hirsch, F.
Publisher: Bocconi University Press ; Springer Verlag
Year: 2011
Subjects: Martingales (Mathematics); Finance Mathematical models; Distribution (Probability theory); Finance; Mathematics
Abstract: 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.
Contents: 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.