Dynamic Markov Bridges and Market Microstructure

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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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.

• Asymmetric Information
• Dynamic Markov Bridges
• Markov Processes
• Stochastic Filtering
• Stochastic Processes
• quantitative finance

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

  Umut Çetin

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

  Albina Danilova

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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