Peacocks and Associated Martingales, with Explicit Constructions - Hirsch, Francis; Profeta, Christophe; Roynette, Bernard; Yor, Marc.; SpringerLink (Online service) (Milano : Springer Milan, 2011)
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$1! = (BThey are developed in eight chapters, with about a hundred of exercises.s
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.
Keywords: Mathematics; Economics, Mathematical; Probabilities; Mathematics; Probability Theory and Stochastic Processes; Quantitative Finance