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We study models of regulatory breakup, in the spirit of Strong and Fouque [Ann. Finance 7 (2011) 349-374] but with a fluctuating number of companies. An important class of market models is based on systems of competing Brownian particles:…
Plasticity with softening and fracture mechanics lead to ill-posed mathematical problems due to the loss of monotonicity. Multiple co-existing solutions are possible when softening elements are coupled together, and solutions cannot be…
Firm growth process in the developing economies is known to produce divergence in their growth path giving rise to bimodality in the size distribution. Similar bimodality has been observed in wealth distribution as well. Here, we introduce…
This paper deals with the stability properties of a closed market, where capital and labour force are acting like a predator-prey system in population-dynamics. The spatial movement of the capital and labour force are taken into account by…
We study the market selection hypothesis in complete financial markets, populated by heterogeneous agents. We allow for a rich structure of heterogeneity: individuals may differ in their beliefs concerning the economy, information and…
We give a new predictive mathematical model for macroeconomics, which deals specifically with asset prices and earnings fluctuations, in the presence of a dynamic economy involving mergers, acquisitions, and hostile takeovers. Consider a…
This paper investigates the dynamics of biomass in a marine ecosystem. A stochastic process is defined in which organisms undergo jumps in body size as they catch and eat smaller organisms. Using a systematic expansion of the master…
We present a novel approach to modeling market dynamics using ordinary differential equations that explicitly incorporates product competitiveness and consumer behavior. Our framework treats market segments as interacting populations in a…
Stochastic versions of a classical model for natural ventilation are proposed and investigated to demonstrate the effect of random fluctuations on stability and predictability. In a stochastic context, the well-known deterministic result…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
We study scenarios where multiple sellers of a homogeneous good compete on prices, where each seller can only sell to some subset of the buyers. Crucially, sellers cannot price-discriminate between buyers. We model the structure of the…
This work's purpose is to understand the dynamics of limit order books in order-driven markets. We try to illustrate a dynamical trading mechanism attached to the microstructure of limit order markets. We capture the iterative nature of…
An agent-based modelling methodology for the joint price evolution of two stocks is put forward. The method models future multidimensional price trajectories reflecting how a class of agents rebalance their portfolios in an operational way…
In the preceding paper we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974--1993. Our results suggest that the data can be described by a scaling approach. Here, we…
In this paper we investigate a dynamic pricing model for constant demand elasticity where customers have a probability distribution on the number of items they order. This is a generalization from standard models which restrict customers to…
We develop a general strategy in order to implement (approximate) discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle equipped with…
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in…
Macroeconomic dynamics is typically modeled under the assumption that the economy evolves according to a single invariant law of motion. This paper shows that this assumption imposes a structural restriction. We develop Dynamic…
Kinetic exchange models have been successful in explaining the shape of the income/wealth distribution in the economies. However, such models usually make some ad-hoc assumptions when it comes to determining the savings factor. Here, we…
We consider a simple analytically tractable model of metastability and ageing. In this model, a particle can jump left or right by two steps to an unoccupied site, but only if the the site in between is occupied. We show that the model is…