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Peacocks and Associated Martingales, with Explicit Constructions
Francis HirschChristophe ProfetaBernard RoynetteMarc Yor
出版Springer Science & Business Media, 2011-05-24
主題Mathematics / Probability & Statistics / GeneralMathematics / AppliedMathematics / Probability & Statistics / Stochastic ProcessesBusiness & Economics / General
ISBN88470190879788847019089
URLhttp://books.google.com.hk/books?id=hix-wkrST00C&hl=&source=gbs_api
EBookSAMPLE
註釋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.