Peacocks and Associated Martingales, with Explicit Constructions
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 …
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- Full title :Peacocks and Associated Martingales, with Explicit Constructions.
Summary
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 eigh.
Read More ↓Edition Statements
- Publication Date:2011.
Publication Statements
- Publisher(s):Springer Milan
- Place of Publication:Milano
- Language:eng
- Publication Date:2011.
Notes
8.2 A General Comparison Theorem for the Upper Orthant Order.
The Physical Object
- Description:1 online resource (411 pages).
Edition Identifiers
- ISBN:8847019079, 9788847019072
- DOI:10.1007/978-88-470-1908-9
- oclc:ocn990476606
- LC Classification:QA273.6
- Dewey Decimal:519.236
Table of Contents
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.
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.
3.1 Martingales Associated to a F2-type Peacock in a Discrete Setting3.…
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