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Dynamic Markov Bridges and Market Microstructure

Theory and Applications

  • Umut Çetin
  • Albina Danilova

Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 90)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Theory

    1. Front Matter
      Pages 1-1
    2. Umut Çetin, Albina Danilova
      Pages 3-21
    3. Umut Çetin, Albina Danilova
      Pages 23-62
    4. Umut Çetin, Albina Danilova
      Pages 63-79
    5. Umut Çetin, Albina Danilova
      Pages 81-117
    6. Umut Çetin, Albina Danilova
      Pages 119-169
  3. Applications

    1. Front Matter
      Pages 171-171
    2. Umut Çetin, Albina Danilova
      Pages 173-189
    3. Umut Çetin, Albina Danilova
      Pages 191-198
    4. Umut Çetin, Albina Danilova
      Pages 199-216
  4. Back Matter
    Pages 217-234

About this book

Introduction

This book undertakes a detailed construction of Dynamic Markov Bridges using a combination of theory and real-world applications to drive home important concepts and methodologies. In Part I, theory is developed using tools from stochastic filtering, partial differential equations, Markov processes, and their interplay. Part II is devoted to the applications of the theory developed in Part I to asymmetric information models among financial agents, which include a strategic risk-neutral insider who possesses a private signal concerning the future value of the traded asset, non-strategic noise traders, and competitive risk-neutral market makers. A thorough analysis of optimality conditions for risk-neutral insiders  is provided and the implications on equilibrium of non-Gaussian extensions are discussed.

A Markov bridge, first considered by Paul Lévy in the context of Brownian motion, is a mathematical system that undergoes changes in value from one state to another when the initial and final states are fixed. Markov bridges have many applications as stochastic models of real-world processes, especially within the areas of Economics and Finance. The construction of a Dynamic Markov Bridge, a useful extension of Markov bridge theory, addresses several important questions concerning how financial markets function, among them: how the presence of an insider trader impacts market efficiency; how insider trading on financial markets can be detected; how information assimilates in market prices; and the optimal pricing policy of a particular market maker.

Principles in this book will appeal to probabilists, statisticians, economists, researchers, and graduate students interested in Markov bridges and market microstructure theory.

Keywords

Asymmetric Information Dynamic Markov Bridges Markov Processes Stochastic Filtering Stochastic Processes

Authors and affiliations

  • Umut Çetin
    • 1
  • Albina Danilova
    • 2
  1. 1.Department of StatisticsLondon School of EconomicsLondonUK
  2. 2.Department of MathematicsLondon School of EconomicsLondonUK

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-8835-8
  • Copyright Information Springer Science+Business Media, LLC, part of Springer Nature 2018
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-8833-4
  • Online ISBN 978-1-4939-8835-8
  • Series Print ISSN 2199-3130
  • Series Online ISSN 2199-3149
  • Buy this book on publisher's site
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