The aim of this work is to establish the personal income distribution from the elementary constituents of a free market; products of a representative good and agents forming the economic network. The economy is treated as a self-organized system. Based on the idea that the dynamics of an economy is governed by slow modes, the model suggests that for short time intervals a fixed ratio of total labour income (capital income) to net income exists (Cobb-Douglas relation). Explicitly derived is...

We propose a stochastic process driven by the memory effect with 718 novel distributions which include both exponential and leptokurtic heavy-tailed distributions. A class of the distributions is analytically derived from the continuum limit of the discrete binary process with the renormalized auto-correlation. The moment generating function with a closed form is obtained, thus the cumulants are calculated and shown to be convergent. The other class of the distributions is numerically...

We derive a new, exact and transparen 7b6 t expansion for option smiles, which lends itself both to analytical approximation and, probably more importantly, to congenial numerical treatments. We show that the skew and the curvature of the smile can be computed as exotic options, for which the Hedged Monte Carlo method is particularly well suited. When applied to options on the S&P index, we find that the skew and the curvature of the smile are very poorly reproduced by the standard Edgeworth...

We consider the problem of the optimal trading strategy in the presence of linear costs, and with a strict cap on the allowed position in the market. Using Bellman's backward recursion method, we show that the optimal strategy is to switch between the maximum allowed long position and the maximum allowed short position, whenever the predictor exce 62e eds a threshold value, for which we establish an exact equation. This equation can be solved explicitely in the case of a discrete...

We consider a 790 simple stochastic model of a urban housing market, in which the interaction of tenants and landlords induces rent (or price) fluctuations. We simulate the model numerically and measure the equilibrium price distribution, which is found to be well-described by a lognormal law. We also study the influence of the density of agents (or equivalently, the vacancy rate) on the price distribution. A simplified version of the model, amenable to analytical treatment, is proposed and...

A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes called driver nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network characteristics on the minimal number of driver nodes required to control a network. We find that clustering and modularity have no discernible impact, but we predict linear, quadratic or no dependence on degree correlations determined by the symmetries...

Network modeling plays a critical role in identifying statistical regularities and structural principles common to many systems. The large majority of recent modeling approaches are connectivity driven, in the sense that the structural pattern of the network is at the basis of the mechanisms ruling the network formation. Connectivity driven models necessarily provide a time-aggregated representation that may fail to describe the instantaneous and fluctuating dynamics of many networks. We...

The occurrence of aftershocks following a major financial crash manifests the critical dynamical response of financial markets. Aftershocks put additional stress on markets, with conceivable dramatic consequences. Such a phenomenon has been shown to be common to most financial assets, both at high and low frequency. Its present-day description relies on an empirical characterization proposed by Omori at the end of 1800 for seismic earthquakes. We point out the limited predictive power in this...

We investigate whether fractal markets hypothesis and its focus on liquidity and invest- ment horizons give reasonable predictions about dynamics of the financial markets during the turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, fractal markets hypothesis considers financial markets as com- plex systems consisting of many heterogenous agents, which are distinguishable mainly with respect to their investment horizon. In the...

We study optimal investment in a financial market having a finite number of assets from a signal processing perspective. We investigate how an investor should distribute capital over these assets and when he should reallocate the distribution of the funds over these assets to maximize the cumulative wealth over any investment period. In particular, we introduce a portfolio selection algorithm that maximizes the expected cumulative wealth in i.i.d. two-asset discrete-time markets where the...