We introduce a simple model of economy, where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading, in such a way that the fundamental symmetry of the economy under an arbitrary change of monetary units is insured. We...

We study Sutton's ‘microcanonical’ model for the internal organization of firms, that leads to non-trivial scaling properties for the statistics of growth rates. We show that the growth rates are asymptotically Gaussian in this model, whereas empirical results suggest that the kurtosis of...

We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of optimal solutions is generally exponentially large, and each...

We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call ‘Principal Regression Analysis’ (PRA) and for which we provide some analytical (using Random Matrix...

We summarize recent research in a rapid growing field, that of statistical finance, also called ‘econophysics’. There are three main themes in this activity: (i) empirical studies and the discovery of interesting universal features in the statistical texture of financial time series, (ii)...

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 decay exponent close to −1.15 at short times, less than ≈ 10<Superscript>3</Superscript> s, and crosses over to a second...</superscript>

While the long-ranged correlation of market orders and their impact on prices has been relatively well studied in the literature, the corresponding studies of limit orders and cancellations are scarce. We provide here an empirical study of the cross-correlation between all these different...

We discuss the general link between mode-coupling like equations (which serve as the basis of some recent theories of supercooled liquids) and the dynamical equations governing mean-field spin-glass models, or the dynamics of a particle in a random potential. The physical consequences of this...

We show that the asymptotic behaviour of the diffusion front in disordered or fractal media is related to the response of the random walk to an applied bias. In general this diffusion front takes the scaled form P(R, t) ∼ 1tvdF ƒ (Rtv), where ν is the diffusion exponent and ƒ(u) behaves as...