Hirsch, Francis.
Peacocks and Associated Martingales, with Explicit Constructions [electronic resource] / by Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor. - XXXII, 388 p. online resource. - B&SS — Bocconi & Springer Series, 2039-1471 . - B&SS — Bocconi & Springer Series, .
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.
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.
9788847019089
10.1007/978-88-470-1908-9 doi
Mathematics.
Finance.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Quantitative Finance.
QA273.A1-274.9 QA274-274.9
519.2
Peacocks and Associated Martingales, with Explicit Constructions [electronic resource] / by Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor. - XXXII, 388 p. online resource. - B&SS — Bocconi & Springer Series, 2039-1471 . - B&SS — Bocconi & Springer Series, .
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.
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.
9788847019089
10.1007/978-88-470-1908-9 doi
Mathematics.
Finance.
Distribution (Probability theory).
Mathematics.
Probability Theory and Stochastic Processes.
Quantitative Finance.
QA273.A1-274.9 QA274-274.9
519.2