Applications of physics to economics and finance: Money, income, wealth, and the stock market

Abstract

Several problems arising in Economics and Finance are analyzed using concepts and quantitative methods from Physics. Here is the abridged abstact: Chapter 1: By analogy with energy, the equilibrium probability distribution of money must follow the exponential Boltzmann-Gibbs law characterized by an effective temperature equal to the average amount of money per economic agent. A thermal machine which extracts a monetary profit can be constructed between two economic systems with different temperatures. Chapter 2: Using data from several sources, it is found that the distribution of income is described for the great majority of population by an exponential distribution, whereas the high-end tail follows a power law. The Lorenz curve and Gini coefficient were calculated and are shown to be in good agreement with both income and wealth data sets. Chapter 3: The Heston model where stock-price dynamics is governed by a geometrical (multiplicative) Brownian motion with stochastic variance is studied. The corresponding Fokker-Planck equation is solved exactly. Integrating out the variance, an analytic formula for the time-dependent probability distribution of stock price changes (returns) is found. The formula is in excellent agreement with the Dow-Jones index for the time lags from 1 to 250 trading days.