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Peacocks and Associated Martingales, with Explicit Constructions

  • Francis Hirsch
  • Christophe Profeta
  • Bernard Roynette
  • Marc Yor

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

  • Francis Hirsch
    • 1
  • Christophe Profeta
    • 2
  • Bernard Roynette
    • 2
  • Marc Yor
    • 3
    • 4
  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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