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© 2011

Peacocks and Associated Martingales, with Explicit Constructions

Book

Part of the B&SS — Bocconi & Springer Series book series (BS)

Table of contents

  1. Front Matter
    Pages i-xxxi
  2. Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 1-86
  3. Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 87-136
  4. Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 137-162
  5. Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 163-179
  6. Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 181-221
  7. Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 223-264
  8. Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 265-336
  9. Francis Hirsch, Christophe Profeta, Bernard Roynette, Marc Yor
    Pages 337-357
  10. Back Matter
    Pages 359-385

About this book

Introduction

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.

Keywords

Brownian motion Convex order Markov processes Martingales Peacocks

Authors and affiliations

  1. 1.Laboratoire d’Analyse et ProbabilitésUniversité d’Évry-Val d’EssonneFrance
  2. 2.Institut Élie CartanUniversité Henri PoincaréNancy
  3. 3.Laboratoire de Probabilités et Modèles AléatoiresUniversité Pierre et Marie CurieParis
  4. 4.Institut Universitaire de FranceFrance

Bibliographic information

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Reviews

From the reviews:

“The authors provide several characterizations of the peacock property, and then continue to provide many different examples of peacocks. … For researchers, the book is a great opportunity to get introduced to this relatively new and fascinating branch of probability theory. For practitioners who want to create models for empirically given marginals (given, e.g., via option prices), the monograph should be a very valuable reference.” (Nicolas Perkowski, Zentralblatt MATH, Vol. 1227, 2012)