E-Book Overview
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.
E-Book Content
Probability Theory and Stochastic Modelling 90
Umut Çetin Albina Danilova
Dynamic Markov Bridges and Market Microstructure Theory and Applications
Probability Theory and Stochastic Modelling Volume 90
Editors-in-chief Peter W. Glynn, Stanford, CA, USA Andreas E. Kyprianou, Bath, UK Yves Le Jan, Orsay, France Advisory Board Søren Asmussen, Aarhus, Denmark Martin Hairer, Coventry, UK Peter Jagers, Gothenburg, Sweden Ioannis Karatzas, New York, NY, USA Frank P. Kelly, Cambridge, UK Bernt Øksendal, Oslo, Norway George Papanicolaou, Stanford, CA, USA Etienne Pardoux, Marseille, France Edwin Perkins, Vancouver, Canada Halil Mete Soner, Zürich, Switzerland
The Probability Theory and Stochastic Modelling series is a merger and continuation of Springer’s two well established series Stochastic Modelling and Applied Probability and Probability and Its Applications series. It publishes research monographs that make a significant contribution to probability theory or an applications domain in which advanced probability methods are fundamental. Books in this series are expected to follow rigorous mathematical standards, while also displaying the expository quality necessary to make them useful and accessible to advanced students as well as researchers. The series covers all aspects of modern probability theory including • • • • • •
Gaussian processes Markov processes Random fields, point processes and random sets Random matrices Statistical mechanics and random media Stochastic analysis
as well as applications that include (but are not restricted to): • Branching processes and other models of population growth • Communications and processing networks • Computational methods in probability and stochastic processes, including simulation • Genetics and other stochastic models in biology and the life sciences • Information theory, signal processing, and image synthesis • Mathematical economics and finance • Statistical methods (e.g. empirical processes, MCMC) • Statistics for stochasti