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We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of…
We propose a generalized diffusion equation for a flat Euclidean space subjected to a continuous infinitesimal scale transform. For the special cases of an algebraic or exponential expansion/contraction, governed by time-dependent scale…
In a multi-channel marketing world, the purchase decision journey encounters many interactions (e.g., email, mobile notifications, display advertising, social media, and so on). These impressions have direct (main effects), as well as…
We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio…
We describe a simple model for speculative trading based on adaptive behavior of economic agents.The adaptive behavior is expressed through a feedback mechanism for changing agents' stock-to-bond ratios, depending on the past performance of…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
In this paper, we examine the long-time dynamics of an epidemic model whose diffusion and reaction terms involve nonlocal effects described by suitable convolution operators.The spreading front of the disease is represented by the free…
This paper involves a diffusive epidemic model whose domain has one free boundary with the Stefan boundary condition, and one fixed boundary subject to the usual homogeneous Dirichlet or Neumann condition. By using the standard upper and…
International trade fluxes evolve as countries revise their portfolios of trade products towards economic development. Accordingly products' shares in international trade vary with time, reflecting the transfer of capital between distinct…
We characterize the different morphological phases that occur in a simple one-dimensional model of propagation of innovations among economic agents [X.\ Guardiola, {\it et. al.}, Phys. Rev E {\bf 66}, 026121 (2002)]. We show that the model…
Lifetime distributions of social entities, such as enterprises, products, and media contents, are one of the fundamental statistics characterizing the social dynamics. To investigate the lifetime distribution of mutually interacting…
In speculative markets, risk-free profit opportunities are eliminated by traders exploiting them. Markets are therefore often described as "informationally efficient", rapidly removing predictable price changes, and leaving only residual…
A dynamical model is introduced for the formation of a bullish or bearish trends driving an asset price in a given market. Initially, each agent decides to buy or sell according to its personal opinion, which results from the combination of…
In this article we revisit the classic problem of tatonnement in price formation from a microstructure point of view, reviewing a recent body of theoretical and empirical work explaining how fluctuations in supply and demand are slowly…
Viral marketing takes advantage of preexisting social networks among customers to achieve large changes in behaviour. Models of influence spread have been studied in a number of domains, including the effect of "word of mouth" in the…
We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final…
We develop from basic economic principles a continuous-time model for a large investor who trades with a finite number of market makers at their utility indifference prices. In this model, the market makers compete with their quotes for the…
This paper studies cost pass-through in differentiated-product oligopoly. I derive a general representation of the pass-through matrix that decomposes equilibrium price responses into the roles of demand curvature, substitution, and…
Standard models of asset price dynamics, such as geometric Brownian motion (see, for example, Osborne, 1959, Samuelson, 2016), do not formally incorporate investor inertia. This paper presents a two-stage framework for modelling this…
In this paper we study the evolution of asset price bubbles driven by contagion effects spreading among investors via a random matching mechanism in a discrete-time version of the liquidity based model of [25]. To this scope, we extend the…