Peacocks and Associated Martingales, with Explicit Constructions - Francis Hirsch, Christophe Profeta, Bernard Roynette & Marc Yor

Peacocks and Associated Martingales, with Explicit Constructions

By Francis Hirsch, Christophe Profeta, Bernard Roynette & Marc Yor

  • Release Date - Published: 2011-05-24
  • Book Genre: Mathematics
  • Author: Francis Hirsch, Christophe Profeta, Bernard Roynette & Marc Yor
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Peacocks and Associated Martingales, with Explicit Constructions Francis Hirsch, Christophe Profeta, Bernard Roynette & Marc Yor read online review & book description:

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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