  The time development of the price of a financial asset is considered by
constructing and solving Langevin equations for a homogeneously saturated
model, and for comparison, for a standard model and for a logistic model. The
homogeneously saturated model uses coupled rate equations for the money supply
and for the price of the asset, similar to the coupled rate equations for
population inversion and power density in a simple model of a homogeneously
broadened laser.
  Predictions of the models are compared for random numbers drawn from a
Student's t-distribution. It is known that daily returns of the DJIA and S&P
500 indices are fat tailed and are described well by Student's t-distributions
over the range of observed values. The homogeneously saturated model shows
returns 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 returns
that are far from consistent with observed daily returns for the indices.
