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Specialized topics on financial data analysis from a numerical and physical point of view are discussed. They pertain to the analysis of crash prediction in stock market indices and to the persistence or not of coherent and random sequences…
We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all…
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 correlated market orders that lead to…
We solve a version of the optimal trade execution problem when the mid asset price follows a displaced diffusion. Optimal strategies in the adapted class under various risk criteria, namely value-at-risk, expected shortfall and a new…
This paper considers the problem of consumption and investment in a financial market within a continuous time stochastic economy. The investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless…
The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the…
The narrow escape problem is a first-passage problem concerned with randomly moving particles in a physical domain, being trapped by absorbing surface traps (windows), such that the measure of traps is small compared to the domain size. The…
This Chapter reviews statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the…
A system manager dynamically controls a diffusion process Z that lives in a finite interval [0,b]. Control takes the form of a negative drift rate \theta that is chosen from a fixed set A of available values. The controlled process evolves…
We analyze an operational policy for a multinational manufacturer to hedge against exchange rate uncertainties and competition. We consider a single product and single period. Because of long-lead times, the capacity investment must done…
This is an invited article for the Discussion and Debate special issue of The European Physical Journal Special Topics on the subject "Can Economics Be a Physical Science?" The first part of the paper traces the personal path of the author…
Several problems arising in Economics and Finance are analyzed using concepts and quantitative methods from Physics. Here is the abridged abstact: Chapter 1: By analogy with energy, the equilibrium probability distribution of money must…
We study the extreme value statistics of first-passage trajectories generating from a one-dimensional drifted Brownian motion subject to stochastic resetting to the starting point with a constant rate $r$. Each stochastic trajectory starts…
In this paper an econophysics model for the currency exchange operations with commission is proposed. With this purpose some analogies and similarities of the processes that take place in the frame of the electrochemical system made from…
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…
Mathematically, the execution of an American-style financial derivative is commonly reduced to solving an optimal stopping problem. Breaking the general assumption that the knowledge of the holder is restricted to the price history of the…
We investigate the limiting distribution of geometric Brownian motion conditional on its running maximum taking large values. We show that the conditional distribution of the geometric Brownian motion converges after a suitable…
Sticky Brownian motion is the simplest example of a diffusion process that can spend finite time both in the interior of a domain and on its boundary. It arises in various applications such as in biology, materials science, and finance.…
A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work,…
Do firm dynamics matter for the transmission of monetary policy? Empirically, the startup rate declines following a monetary contraction, while the exit rate increases, both of which reduce aggregate employment. I present a model that…