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The time development of the price of a financial asset is considered byconstructing and solving Langevin equations for a homogeneously saturatedmodel, and for comparison, for a standard model and for a logistic model. Thehomogeneously saturated model uses coupled rate equations for the money supplyand for the price of the asset, similar to the coupled rate equations forpopulation inversion and power density in a simple model of a homogeneouslybroadened laser.  Predictions of the models are compared for random numbers drawn from aStudent's t-distribution. It is known that daily returns of the DJIA and S&P500 indices are fat tailed and are described well by Student's t-distributionsover the range of observed values. The homogeneously saturated model showsreturns that are consistent with daily returns for the indices (in the range of-30% to +30%) whereas the standard model and the logistic model show returnsthat are far from consistent with observed daily returns for the indices.

Homogeneously Saturated Model for Development in Time of the Price of an Asset