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…

Boundary-induced apparent risk aversion in non-ergodic growth models.

Study on multiplicities in length spectrum of Salem numbers.

Grimaldi-Pansu metrics are constructed for manifolds with multiple ends.

The paper introduces a method for forecasting corporate sales growth using multiple reference variables.

Study on volume growth of horospheres in specific Heintze groups.

Bubbles are essential in certain economic models with high growth and low interest rates.

In this paper we provide a general solution for the dividend discount model in order to compute the intrinsic value of a common stock that allows for multiple stage growth rates of any predetermined number of periods. A mathematical proof is provided for the suggested general solution. A numerical application is also p…

Framework generates realistic crop images for growth modeling.

Some agent-based models for growth and allocation of resources are described. The first class considered consists of conservative models, where the number of agents and the size of resources are constant during time evolution. The second class is made up of multiplicative noise models and some of their extensions to co…

We consider the problem of finding optimal strategies that maximize the average growth-rate of multiplicative stochastic processes. For a geometric Brownian motion the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction o…

We introduce a criterion how to price derivatives in incomplete markets, based on the theory of growth optimal strategy in repeated multiplicative games. We present reasons why these growth-optimal strategies should be particularly relevant to the problem of pricing derivatives. We compare our result with other alterna…

We investigate the growth optimal strategy over a finite time horizon for a stock and bond portfolio in an analytically solvable multiplicative Markovian market model. We show that the optimal strategy consists in holding the amount of capital invested in stocks within an interval around an ideal optimal investment. Th…

Revisits granular models explaining firm growth rates and sizes.

Quadratic growth of intersecting curves on surfaces resolved.

Stable cooperation emerges in fluctuating environments.

Using the method of Nehari manifold, we prove the existence of at least two distinct weak solutions to elliptic equation of four order with singulatities and with critical Sobolev growth.

Integral foliated simplicial volume is zero for certain amenable covers.

In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and "shape". We show t…

Let $G$ be a finite group with symmetric generating set $S$, and let $c = \max_{R > 0} |B(2R)|/|B(R)|$ be the doubling constant of the corresponding Cayley graph, where $B(R)$ denotes an $R$-ball in the word-metric with respect to $S$. We show that the multiplicity of the $k$th eigenvalue of the Laplacian on the Cayley…

We suggest an analytical approach for Pareto-Zipf law, where we assume random multiplicative noise and fragmentation processes for the growth of the number of citizens of each city and the number of the cities, respectively.

There is, among the economist ecosystem, the idea of virtuous public spending as a form of promotion of economic growth. If we think on the way GDP is measured, it is not possible to get that conclusion because it becomes circular: measuring the money flow obviously will detect directly the public spending but always m…

This paper investigates integer multiplication of continued fractions using geometric structures. In particular, this paper shows that integer multiplication of a continued fraction can be represented by replacing one triangulation of an orbifold with another triangulation. This method is used to show that eventually p…

We demonstrate by mathematical analysis and systematic computer simulations that redistribution can lead to sustainable growth in a society. The human capital dynamics of each agent is described by a stochastic multiplicative process which, in the long run, leads to the destruction of individual human capital and the e…

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various ki…

Paper proposes active learning for structured output design, improving Gaussian process model predictions.

Credit expansion led to stronger household leverage cycles during the U.S. business cycle.

In the recent paper \cite{LoD1}, we classified closed geodesics on Finsler manifolds into rational and irrational two families, and gave a complete understanding on the index growth properties of iterates of rational closed geodesics. This study yields that a rational closed geodesic can not be the only closed geodesic…

New bounds on homological eigenvalues relate to Weil-Petersson length.

The study examines the growth of reciprocal classes in Hecke groups, proving an asymptotic formula.

Study on Lane-Emden equation on curved spaces, revealing new existence and non-existence phenomena.

In this paper, a new theory is developed for first-order stochastic convex optimization, showing that the global convergence rate is sufficiently quantified by a local growth rate of the objective function in a neighborhood of the optimal solutions. In particular, if the objective function $F(\mathbf w)$ in the $ε$-sub…

We report quantitative relations between corruption level and economic factors, such as country wealth and foreign investment per capita, which are characterized by a power law spanning multiple scales of wealth and investments per capita. These relations hold for diverse countries, and also remain stable over differen…

We study long-term growth-optimal strategies on a simple market with linear proportional transaction costs. We show that several problems of this sort can be solved in closed form, and explicit the non-analytic dependance of optimal strategies and expected frictional losses of the friction parameter. We present one der…

Cooperation is a persistent behavioral pattern of entities pooling and sharing resources. Its ubiquity in nature poses a conundrum. Whenever two entities cooperate, one must willingly relinquish something of value to the other. Why is this apparent altruism favored in evolution? Classical solutions assume a net fitness…

We relate small 1-form Laplacian eigenvalues to relative cycle complexity on closed hyperbolic manifolds: small eigenvalues correspond to closed geodesics no multiple of which bounds a surface of small genus. We describe potential applications of this equivalence principle toward proving optimal torsion homology growth…

Almost-isometries are quasi-isometries with multiplicative constant one. Lifting a pair of metrics on a compact space gives quasi-isometric metrics on the universal cover. Under some additional hypotheses on the metrics, we show that there is no almost-isometry between the universal covers. We show that Riemannian mani…

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

In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loos…

Let $n$, $q$ and $r$ be positive integers, and let $K_N^n$ be the $n$-skeleton of an $(N-1)$-simplex. We show that for $N$ sufficiently large every embedding of $K_N^n$ in $\mathbb{R}^{2n+1}$ contains a link $L_1\cup\cdots\cup L_r$ consisting of $r$ disjoint $n$-spheres, such that the linking number $link(L_i,L_j)$ is …

Following the work of Okuyama, Takayasu and Takayasu [Okuyama, Takayasu and Takayasu 1999] we analyze huge databases of Japanese companies' financial figures and confirm that the Zipf's law, a power law distribution with the exponent -1, has been maintained over 30 years in the income distribution of Japanese companies…

A new model that combines economic growth rate fluctuations at the microscopic and macroscopic level is presented. At the microscopic level, firms are growing at different rates while also being exposed to idiosyncratic shocks at the firm and sector level. We describe such fluctuations as independent Lévy-stable fluctu…

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…

Abstract Coxeter groups have growth rates that are Perron numbers.

PoDiRe learns long-term rewards in multi-task recommendations.

We introduce a mean-field type approximation for description of company's income statistics. Utilizing huge company data we show that a discrete version of Langevin equation with additive and multiplicative noises can appropriately describe the time evolution of a company's income fluctuation in statistical sense. The …

Historical economic growth in countries of the former USSR is analysed. It is shown that Unified Growth Theory is contradicted by the data, which were used, but not analysed, during the formulation of this theory. Unified Growth Theory does not explain the mechanism of economic growth. It explains the mechanism of Malt…

The paper develops methods to identify stable associations across multiple studies.