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.
- ISBN13 9788847025196
- Publish Date 15 July 2013 (first published 24 May 2011)
- Publish Status Active
- Publish Country IT
- Imprint Springer Verlag
- Edition 2011 ed.
- Format Paperback
- Pages 388
- Language English