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In this paper we propose a stochastic model to analyze the time evolution of inequality within an economic system. The classical inequality indices, Herfindahl-Hirschman, Gini and Theil’s entropy, are thereby turned into a dynamic form. We show, by using a simulative approach, how it is possible to study the time evolution of inequality in a closed or open economy. We pay particular attention to immigration effects on the inequality. The model is able to manage different behaviors of the inequality indices and it may help decision makers calibrate the economic policies of inequality containment.

In this paper, a full treatment of homogeneous discrete time Markov reward processes is presented. The higher order moments of the homogeneous reward process are determined. In the last part of the paper, an application to the bonus-malus car insurance is presented. The application was constructed using real data.