Peacocks and Associated Martingales, with Explicit Constructions (Hardcover)

Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor

  • 出版商: Springer
  • 出版日期: 2011-05-24
  • 售價: $5,010
  • 貴賓價: 9.5$4,760
  • 語言: 英文
  • 頁數: 388
  • 裝訂: Hardcover
  • ISBN: 8847019079
  • ISBN-13: 9788847019072

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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.