Dynamic Markov Bridges and Market Microstructure

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.

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

Autorentext
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.

Zusammenfassung
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;

Inhalt
Markov processes.- Stochastic Differential Equations and Martingale Problems.- Stochastic Filtering.- Static Markov Bridges and Enlargement of Filtrations.- Dynamic Bridges.- Financial markets with informational asymmetries and equilibrium.- Kyle-Back model with dynamic information: no default case.- Appendix A.