Peacocks and Associated Martingales, with Explicit Constructions

'Peacocks' and their associated mathematical phenomena, 'martingales', play a key role in the mathematics of finance. This monograph uses a variety of methods from time inversion to Skorokhod embeddings in its exploration of peacocks and martingales.

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.

First book on this topic A remarkable range of probabilistic tools Numerous exercises with hints Includes supplementary material: sn.pub/extras

Inhalt
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.