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Using duality theory techniques we derive simple, closed-form formulas for bounding the optimal revenue of a monopolist selling many heterogeneous goods, in the case where the buyer's valuations for the items come i.i.d. from a uniform…
We introduce a new, probability-level approach to calculations in scalar field particle scattering. The approach involves the implicit summation over final states, which makes causality manifest since retarded propagators emerge naturally.…
We provide an exact solution to the ideal-gas-like models studied in econophysics to understand the microscopic origin of Pareto-law. In these class of models the key ingredient necessary for having a self-organized scale-free steady-state…
The amount of information propagated by an intermediate heavy particle exhibits characteristic features in inelastic scatterings with $n\geq 3$ final particles. As the total energy increases, the entanglement entropy, between its decay…
We propose a set of conservative models in which agents exchange wealth with a preference in the choice of interacting agents in different ways. The common feature in all the models is that the temporary values of financial status of agents…
A government has to finance a risk for its population. It shares the charges among the population with a fixed scale based on economic criteria. Various organisms have to collect and to redistribute fairly the subsidies. Under these…
Using the matrix product formalism we formulate a natural p-species generalization of the asymmetric simple exclusion process. In this model particles hop with their own specific rate and fast particles can overtake slow ones with a rate…
How can we limit wealth disparities while stimulating economic flows in sustainable societies? To examine the link between these concepts, we propose an econophysics asset exchange model with the surplus stock of the wealthy. The wealthy…
In this paper, our aim is to investigate necessary conditions for optimal investment. We model the wealth process by Backward differential stochastic equations (shortly for BSDE) with or without constraints on wealth and portfolio process.…
We analyze the household savings problem in a general setting where returns on assets, non-financial income and impatience are all state dependent and fluctuate over time. All three processes can be serially correlated and mutually…
The paper starts with a brief review of present understanding of income distributions; especially with regard to recent work in the field of econophysics that draws parallels between income, wealth and energy distributions. Examples of…
In this paper we extend the series of our studies on the properties of an interacting particle model for market microstructure. In our earlier work we defined a Markov process on the majority opinion of the agents, obtained the transition…
We investigate the uniform reshuffling model for money exchanges: two agents picked uniformly at random redistribute their dollars between them. This stochastic dynamics is of mean-field type and eventually leads to a exponential…
In this paper, based on the analysis of the formula (2.2) for calculating the elastic scattering diagrams of microparticles on a multilayer crystal surface, derived by the author in the article [3], it is shown that the stochastic approach…
In this invited book chapter, we draw the reader to a brief review of the different Kinetic Exchange Models (KEMs) that have gradually developed for markets and how they can be employed to quantitatively study inequalities (the Gini Index…
The inequality of wealth distribution is a universal phenomenon in the civilized nations, and it is often imputed to the Matthew effect, that is, the rich get richer and the poor get poorer. Some philosophers unjustified this phenomenon and…
We introduce three models of fragmentation in which the largest fragment in the system can be broken at each time step with a fixed probability, p. We solve these models exactly in the long time limit to reveal stable time invariant…
There are two fair ways to distribute particles in boxes. The first way is to divide the particles equally between the boxes. The second way, which is calculated here, is to score fairly the particles between the boxes. The obtained power…
We formulate a flexible micro-to-macro kinetic model which is able to explain the emergence of income profiles out of a whole of individual economic interactions. The model is expressed by a system of several nonlinear differential…
The effects of saving and spending patterns on holding time distribution of money are investigated based on the ideal gas-like models. We show the steady-state distribution obeys an exponential law when the saving factor is set uniformly,…