Format:
Online-Ressource (430p. 11 illus., 6 illus. in color, digital)
ISBN:
9788847019089
Series Statement:
B&SS — Bocconi & Springer Series
Content:
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.
Content:
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.
Note:
Includes bibliographical references and index
,
Title Page; Copyright Page; Table of Contents; A Few Words of Explanation; Associated Processes; Diverse Appreciations of Peacocks; Introduction; Peacocks, Associated Martingales and Mathematical Finance; Chapter 1: Some Examples of Peacocks; Chapter 2: The Sheet Method; Chapter 3: The Time Reversal Method; Chapter 4: The Time Inversion Method; Chapter 5: The Sato Process Method; Chapter 6: The SDE Method; Chapter 7: The Skorokhod Embedding (SE) Method; Chapter 8: Comparing Multidimensional Marginals; Acknowledgements; Terminology about: Association, Attachment, Extension
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Associated ProcessesAttached Processes; Extending Processes; 1 Some Examples of Peacocks; 1.1 Introduction; 1.2 Examples of Peacocks; 1.3 Peacocks in a Gaussian Setting; 1.4 Peacocks in a Markovian Set-up; Notes and Comments; 2 The Sheet Method; 2.1 General Framework; 2.2 The Brownian Sheet Method; 2.3 Space-time Harmonic Functions for the Brownian Sheet (STHBS) and Peacocks; 2.4 The L´evy Sheet Method; 2.5 Space-Time Harmonic Functions for W(L) and Peacocks; 2.6 Peacocks and Gaussian Sheets; Notes and Comments; 3 The Time Reversal Method
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3.1 Martingales Associated to a F2-type Peacock in a Discrete Setting3.2 Martingales Associated to a F2-type Peacock in a Brownian Setting; 3.3 Harmonic Functions in Rn\{0} and Peacocks; 3.4 Martingales Associated to a F2-type Peacock in a L´evy Process Framework; 3.5 Peacocks and Martingales Indexed by Some Predictable Processes; 3.6 The Time Reversal Method in a More General Set-up; Notes and Comments; 4 The Time Inversion Method; 4.1 Martingale Constructed from an Integrable L´evy Process by Time Inversion; 4.2 Feller's Process and F1-type Peacocks
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4.3 Continuous Space Branching Processes (CSBP) and F1-type Peacocks4.4 A Scaling Property Extension of the Previous Results; Notes and Comments; 5 The Sato Process Method; 5.1 Introduction; 5.2 Self-Decomposability and Sato Processes; 5.3 Sato Processes and Peacocks; 5.4 Quadratic Functionals of Bessel Processes (RN(t), t = 0); 5.5 The Sato Sheet Method; Notes and Comments; 6 The Stochastic Differential Equation Method; 6.1 M. Pierre's Uniqueness Theorem for a Fokker-Planck Equation; 6.2 The Fokker-Planck Equation Method; 6.3 Martingales Associated to (f(Bt), t = 0)
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6.4 Martingales Associated to Solutions of Some SDE's6.5 A Variant of the Fokker-Planck Equation Method; 6.6 Martingales Associated to the Processes (vtX, t = 0); 6.7 Peacocks and the Porous Media Equation; Notes and Comments; 7 The Skorokhod Embedding (SE) Method; 7.1 Introduction; 7.2 Construction of Randomized SE's; 7.3 Hall's Method for SE; 7.4 The Az´ema-Yor Algorithm for SE; 7.5 Bass' Method; 7.6 The Ocone Martingale Method; 7.7 Student's Peacocks; Notes and Comments; 8 Comparison of Multidimensional Marginals; 8.1 Introduction
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8.2 A General Comparison Theorem for the Upper Orthant Order
Additional Edition:
ISBN 9788847019072
Additional Edition:
Buchausg. u.d.T. Peacocks and associated martingales, with explicit constructions Milan [etc.] : Springer, 2011 ISBN 8847019079
Additional Edition:
ISBN 9788847019072
Language:
English
Subjects:
Mathematics
Keywords:
Martingal
;
Martingal
DOI:
10.1007/978-88-470-1908-9
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Author information:
Yor, Marc 1949-2014
Author information:
Roynette, Bernard
