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We provide a theoretical framework to understand when firms may benefit from exploiting previously abandoned technologies and brands. We model for the long run process of innovation, allowing for sustainable diversity and comebacks of old…
The financial market is nonpredictable, as according to the Bachelier, the mathematical expectation of the speculator is zero. Nevertheless, we observe in the price fluctuations the two distinct scales, short and long time. Behaviour of a…
We introduce a new diffusion process Xt to describe asset prices within an economic bubble cycle. The main feature of the process, which differs from existing models, is the drift term where a mean-reversion is taken based on an exponential…
We use standard physics techniques to model trading and price formation in a market under the assumption that order arrival and cancellations are Poisson random processes. This model makes testable predictions for the most basic properties…
Most theoretical analysis for lifetime distribution explains origins of specific distribution based on independent failure. We develop a unified framework encompassing different lifetime distribution for failure-coupled network systems. We…
In order to describe the properties of the observed distribution of wealth in a population, most economic models rely on the existence of an asymptotic equilibrium state. In addition, the process generating the equilibrium distribution is…
This paper continues the study, initiated by Cole and Fleischer, of the behavior of a tatonnement price update rule in Ongoing Fisher Markets. The prior work showed fast convergence toward an equilibrium when the goods satisfied the weak…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional…
We consider a decision maker who must choose an action in order to maximize a reward function that depends also on an unknown parameter {\Theta}. The decision maker can delay taking the action in order to experiment and gather additional…
We propose a minimal theory of non-linear price impact based on a linear (latent) order book approximation, inspired by diffusion-reaction models and general arguments. Our framework allows one to compute the average price trajectory in the…
A percolation model is presented, with computer simulations for illustrations, to show how the sales of a new product may penetrate the consumer market. We review the traditional approach in the marketing literature, which is based on…
In this work, we consider a continuous-time inventory system where the demand process follows an inventory-dependent diffusion process. The ordering cost of each order depends on the order quantity and is given by a general function, which…
This paper studies identification and estimation of a dynamic discrete choice model of demand for differentiated product using consumer-level panel data with few purchase events per consumer (i.e., short panel). Consumers are…
Bacterial populations in natural conditions are expected to experience stochastic environmental fluctuations, and in addition, environments are affected by bacterial activities since they consume substrates and excrete various chemicals. We…
Understanding whether a population will survive and flourish or become extinct is a central question in population biology. One way of exploring this question is to study population dynamics using reaction-diffusion equations, where…
We introduce a mathematical model on the dynamics of demand and supply incorporating collectability and saturation factors. Our analysis shows that when the fluctuation of the determinants of demand and supply is strong enough, there is…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
Constraints can affect dramatically the behavior of diffusion processes. Recently, we analyzed a natural and a technological system and reported that they perform diffusion-like discrete steps displaying a peculiar constraint, whereby the…
We study the properties of nonequilibrium systems modelled as spin models without defined Hamiltonian as the majority voter model. This model has transition probabilities that do not satisfy the condition of detailed balance. The lack of…