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Dynamic Markov Bridges and Market Microstructure

Theory and Applications

  • Book
  • © 2018

Overview

Authors:
  1. Umut Çetin

    1. Department of Statistics, London School of Economics, London, UK

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    You can also search for this author in PubMed   Google Scholar

  2. Albina Danilova

    1. Department of Mathematics, London School of Economics, London, UK

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    You can also search for this author in PubMed   Google Scholar

  • Cutting-edge interdisciplinary research in the areas of applied statistics, mathematics, finance, and economics
  • First comprehensive text on using Dynamic Markov Bridges to study asymmetric information among market participants
  • Offers real-world applications of Markov processes to explain and evaluate market microstructure models
  • Examines the case of risk-averse market makers and their implications on equilibrium pricing

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

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiv
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  2. Theory

    1. Front Matter

      Pages 1-1
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    2. Markov Processes

      • Umut Çetin, Albina Danilova
      Pages 3-21

    3. Stochastic Differential Equations and Martingale Problems

      • Umut Çetin, Albina Danilova
      Pages 23-62

    4. Stochastic Filtering

      • Umut Çetin, Albina Danilova
      Pages 63-79

    5. Static Markov Bridges and Enlargement of Filtrations

      • Umut Çetin, Albina Danilova
      Pages 81-117

    6. Dynamic Bridges

      • Umut Çetin, Albina Danilova
      Pages 119-169

  3. Applications

    1. Front Matter

      Pages 171-171
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    2. Financial Markets with Informational Asymmetries and Equilibrium

      • Umut Çetin, Albina Danilova
      Pages 173-189

    3. Kyle—Back Model with Dynamic Information: No Default Case

      • Umut Çetin, Albina Danilova
      Pages 191-198

    4. Kyle—Back Model with Default and Dynamic Information

      • Umut Çetin, Albina Danilova
      Pages 199-216

  4. Back Matter

    Pages 217-234
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Keywords

About this book

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 undergoeschanges 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.

Authors and Affiliations

  • Department of Statistics, London School of Economics, London, UK

    Umut Çetin

  • Department of Mathematics, London School of Economics, London, UK

    Albina Danilova

About the authors

Umut Çetin is Professor of Statistics at the London School of Economics, where he is also Co-director of the Financial Mathematics and Statistics bachelor's program. His research interests include stochastic calculus, theory of martingales and Markov processes, linear and nonlinear filtering and market microstructure. He has published numerous papers in peer-reviewed journals, including Springer’s Finance and Stochastics.

Albina Danilova is Associate Professor of Mathematics at the London School of Economics (LSE). Her research interests span asymmetric information models, market microstructure, stochastic control, and equilibrium theory.

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