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Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
Abstract The subject of this paper is the evolution of Brownian particles in disordered environments. The “Ariadne's clew” we follow is understanding of the general statistical mechanisms which may
How Markets Slowly Digest Changes in Supply and Demand
In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how
Noise Dressing of Financial Correlation Matrices
We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price
Fluctuations and Response in Financial Markets: The Subtle Nature of 'Random' Price Changes
Using Trades and Quotes data from the Paris stock market, we show that the random walk nature of traded prices results from a very delicate interplay between two opposite tendencies: long-range
Statistical properties of stock order books: empirical results and models
Abstract We investigate several statistical properties of the order book of three liquid stocks of the Paris Bourse. The results are to a large degree independent of the stock studied. The most
Critical reflexivity in financial markets: a Hawkes process analysis
We model the arrival of mid-price changes in the E-mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a
Theory of financial risks : from statistical physics to risk management
1. Probability theory: basic notions 2. Statistics of real prices 3. Extreme risks and optimal portfolios 4. Futures and options: fundamental concepts 5. Options: some more specific problems Glossary.
Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management
Foreword Preface 1. Probability theory: basic notions 2. Maximum and addition of random variables 3. Continuous time limit, Ito calculus and path integrals 4. Analysis of empirical data 5. Financial
Theory Of Financial Risk And Derivative Pricing
Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the