arXiv research

Effects of randomness on non-integer power law tails in multiplicatively interacting stochastic processes are investigated theoretically. Generally, randomness causes decrease of the exponent of tails and the growth rate of processes. Explicit calculations are performed for two examples: uniformly distributed and two p…

LMC algorithm achieves efficient sampling from complex distributions with specific tail behaviors.

Revisits granular models explaining firm growth rates and sizes.

Study finds sales forecasters overreact to extreme news.

Study growth patterns in random networks using i.i.d. perturbations.

Study Hilbert's projective metric for bounded growth functions leading to Sinkhorn's algorithm convergence.

We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation of the expression describing the declining long-term tail of a social discount c…

We analyze the fluctuations in the gross domestic product (GDP) of 152 countries for the period 1950--1992. We find that (i) the distribution of annual growth rates for countries of a given GDP decays with ``fatter'' tails than for a Gaussian, and (ii) the width of the distribution scales as a power law of GDP with a s…

We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety…

We introduce a model of proportional growth to explain the distribution of business firm growth rates. The model predicts that the distribution is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent 3. Because of data limitations, previous studies in this field hav…

This paper investigates the statistical properties of within-country GDP and industrial production (IP) growth rate distributions. Many empirical contributions have recently pointed out that cross-section growth rates of firms, industries and countries all follow Laplace distributions. In this work, we test whether als…

We introduce a simple agent-based model which allows us to analyze three stylized facts: a fat-tailed size distribution of companies, a `tent-shaped' growth rate distribution, the scaling relation of the growth rate variance with firm size, and the causality between them. This is achieved under the simple hypothesis th…

We introduce a model of proportional growth to explain the distribution $P(g)$ of business firm growth rates. The model predicts that $P(g)$ is Laplace in the central part and depicts an asymptotic power-law behavior in the tails with an exponent $ζ=3$. Because of data limitations, previous studies in this field have b…

We study and generalize in various ways the model of rational expectation (RE) bubbles introduced by Blanchard and Watson in the economic literature. First, bubbles are argued to be the equivalent of Goldstone modes of the fundamental rational pricing equation, associated with the symmetry-breaking introduced by non-va…

This paper analyzes the equilibrium distribution of wealth in an economy where firms' productivities are subject to idiosyncratic shocks, returns on factors are determined in competitive markets, dynasties have linear consumption functions and government imposes taxes on capital and labour incomes and equally redistrib…

Is the large influence that mutual funds assert on the U.S. financial system spread across many funds, or is it is concentrated in only a few? We argue that the dominant economic factor that determines this is market efficiency, which dictates that fund performance is size independent and fund growth is essentially ran…

We determine the distribution of size and growthrates of German business firms in 1987-1997. We find a log-normal size distribution. The distribution of growth rates has fat tails. It can be fitted to an exponential in a narrow central region and is dominated by finite-sample-size effects far in its wings. We study the…

Study of deep Stable neural networks with various activation functions.

We investigate the ergodic problem of growth-rate maximization under a class of risk constraints in the context of incomplete, Itô-process models of financial markets with random ergodic coefficients. Including {\em value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited expected loss} (LEL), these cons…

Investors target specific regions of payoff distributions for portfolio optimization.

A modular cash-overlay rule for allocating between a fixed growth-defensive risky sleeve and interest-bearing cash.

We present a preferential attachment growth model to obtain the distribution $P(K)$ of number of units $K$ in the classes which may represent business firms or other socio-economic entities. We found that $P(K)$ is described in its central part by a power law with an exponent $φ=2+b/(1-b)$ which depends on the probabil…

This paper proposes non-stationary factor models for financial stress in the UK.

This paper describes an agent-based model of interacting firms, in which interacting firm agents rationally invest capital and labor in order to maximize payoff. Both transactions and production are taken into account in this model. First, the performance of individual firms on a real transaction network was simulated.…

Hybrid model improves synthetic equity data generation.

New insights into natural exponential families improve regret bounds for bandit problems.

Detailed empirical studies of publicly traded business firms have established that the standard deviation of annual sales growth rates decreases with increasing firm sales as a power law, and that the sales growth distribution is non-Gaussian with slowly decaying tails. To explain these empirical facts, a theory is dev…

Paper introduces machine learning for time series data, improving nowcasting accuracy.

We use the P&L on a particular class of swaps, representing variance and higher moments for log returns, as estimators in our empirical study on the S&P500 that investigates the factors determining variance and higher-moment risk premia. This class is the discretisation invariant sub-class of swaps with Neuberger's agg…

Using public data (Forbes Global 2000) we show that the asset sizes for the largest global firms follow a Pareto distribution in an intermediate range, that is ``interrupted'' by a sharp cut-off in its upper tail, where it is totally dominated by financial firms. This flattening of the distribution contrasts with a lar…

RELTA-SGLD stabilizes nonconvex SGLD updates with a lighter taming scheme.

We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in the cases $K=1$ and $K \to \infty$. The resulting stationary distribution of siz…

We propose and study a simple model of dynamical redistribution of capital in a diversified portfolio. We consider a hypothetical situation of a portfolio composed of N uncorrelated stocks. Each stock price follows a multiplicative random walk with identical drift and dispersion. The rules of our model naturally give r…

Growth rate of real GDP per capita is represented as a sum of two components -- a monotonically decreasing economic trend and fluctuations related to a specific age population change. The economic trend is modeled by an inverse function of real GDP per capita with a numerator potentially constant for the largest develo…

We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over Aug 1998 - Oct 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio…

The study shows that the visible range from a point on harmonic manifolds follows an exponential distribution.

By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is independent of the firm's size (Gibrat's law of proportionate effect). We also find t…

We extend the model of rational bubbles of Blanchard and of Blanchard and Watson to arbitrary dimensions d: a number d of market time series are made linearly interdependent via d times d stochastic coupling coefficients. We first show that the no-arbitrage condition imposes that the non-diagonal impacts of any asset i…

A bipartite producer-consumer network is constructed to describe the industrial structure. The edges from consumer to producer represent the choices of the consumer for the final products and the degree of producer can represent its market share. So the size distribution of firms can be characterized by producer's degr…

Many studies in Economics and other disciplines have been reporting distributions following power-law behavior (i.e distributions of incomes (Pareto's law), city sizes (Zipf's law), frequencies of words in long sequences of text etc.)[1, 6, 7]. This widespread observed regularity has been explained in many ways: genera…

Model quantifies cyber-attacks' impact on firms and insurers.

New algorithm extends LMC to more complex potentials.

We empirically verify that the market capitalisations of coins and tokens in the cryptocurrency universe follow power-law distributions with significantly different values, with the tail exponent falling between 0.5 and 0.7 for coins, and between 1.0 and 1.3 for tokens. We provide a rationale for this, based on a simpl…

An analytic model is presented that considers the evolution of a market of durable goods. The model suggests that after introduction goods spread always according to a Bass diffusion. However, this phase will be followed by a diffusion process for durable consumer goods governed by a variation-selection-reproduction me…

Multi-agent models have been used in many contexts to study generic collective behavior. Similarly, complex networks have become very popular because of the diversity of growth rules giving rise to scale-free behavior. Here we study adaptive networks where the agents trade ``wealth'' when they are linked together while…

Critical volatility triggers log-normal to power-law transitions in interconnected systems.

HS-BQR extends horseshoe prior for Bayesian quantile regression.

New method models fat-tailed distributions with anisotropic tail-adaptive flows.