Stochastic processes in the social sciences

The present work uses statistical mechanics tools to investigate the dynamics of markets, prices, trades and wealth distribution. We studied the evolution of market dynamics in different stages of historical development by analyzing commodity prices from two distinct periods : ancient Babylon, and medieval and early modern England. We find that the first-digit distributrions of both Babylon and England commodity prices follow Benford's Law, indicating that the data represent empirical observations typically arising from a free market. Further, we find that the normalized prices of both Babylon and England agricultural commodities are characterized by stretched exponential distributions, and exhibit persistent correlations of a power law type over long periods of up to several centuries, in contrast to contemporary markets. Our findings suggest that similar market interactions may underlie the dynamics of ancient agricultural commodity prices, and that these interactions may remain stable across centuries. To further investigate the dynamics of markets, we present the analogy between transfers of money between individuals and the transfer of energy through particle collisions by means of the kinetic theory of gases. We introduce a theoretical framework of how micro rules of trading lead to the emergence of income and wealth distribution. Particularly, we study the effects of different types of distribution of savings/investments among individuals in a society and different welfare/subsidies redistribution policies. Results show that while considering savings propensities, the models approach empirical distributions of wealth quite well. The effect of redistribution better captures specific features of the distributions which earlier models failed to do. Moreover, the models still preserve the exponential decay observed in empirical income distributions reported by tax data and surveys.