Peacocks and associated martingales, with explicit constructions
By: Francis Hirsch ... [et al.].
Series: B&SS -- Bocconi & Springer series -- 3; Bocconi & Springer series -- 3.
Publisher: Bocconi University Press; Springer Verlag
Published: 2011
Place of publication: [Milan, Italy]; Milan; New York
Language: eng
Number of pages: 384
ISBN-13: 9788847019072; 9788847019089
Subjects: Mathematical models; Distribution (Probability theory); Martingales (Mathematics); Finance
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.
Notes: Includes bibliographical references (p. [373]-381) and index.