Related papers: On Convergence in the Spatial AK Growth Models
We study the problem of minimizing the sum of potentially non-differentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the…
This paper is based on the premise that economic growth is driven by an interplay between innovation and imitation in an economy composed of interacting firms operating in a stochastic environment. A novel approach to modeling imitation is…
In this paper, we study the portfolio optimization problem with general utility functions and when the return and volatility of underlying asset are slowly varying. An asymptotic optimal strategy is provided within a specific class of…
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…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…
Our main contribution in this article is the achievement of the turnpike property in its integral and exponential forms for parameter-dependent systems with averaged observations in the cost functional. Namely, under suitable assumptions…
Spatial autoregressive combined (SAC) model has been widely studied in the literature for the analysis of spatial data in various areas such as geography, economics, demography, regional sciences. This is a linear model with scalar…
Economic growth is unpredictable unless demand is quantified. We solve this problem by introducing the demand for unpaid spare time and a user quantity named human capacity. It organizes and amplifies spare time required for enjoying…
A standard belief on emerging collective behavior is that it emerges from simple individual rules. Most of the mathematical research on such collective behavior starts from imperative individual rules, like always go to the center. But how…
We propose a general scenario to analyze social and economic changes in modern environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time,…
A population is said to have an ideal free distribution in a spatially heterogeneous but temporally constant environment if each of its members have chosen a fixed spatial location in a way that optimizes its individual fitness, allowing…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
An array system of coupled maps is proposed as a model for economy evolution. The local dynamics of each map or agent is controlled by two parameters. One of them represents the growth capacity of the agent and the other one is a control…
Motivated by the fact that circular or spherical data are often much concentrated around a location $\pmb\theta$, we consider inference about $\pmb\theta$ under "high concentration" asymptotic scenarios for which the probability of any…
We consider an agent who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost. The utility function considered is…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
An urban planner might design the spatial layout of transportation amenities so as to improve accessibility for underserved communities -- a fairness objective. However, implementing such a design might trigger processes of neighborhood…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
We consider a certain lattice branching random walk with on-site competition and in an environment which is heterogeneous at a macroscopic scale $1/\varepsilon$ in space and time. This can be seen as a model for the spatial dynamics of a…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…