  We present a stochastic, agent-based, binary-transaction Asset-Exchange Model
(AEM) for wealth distribution that allows for agents with negative wealth. This
model retains certain features of prior AEMs such as redistribution and
wealth-attained advantage, but it also allows for shifts as well as scalings of
the agent density function. We derive the Fokker-Planck equation describing its
time evolution and we describe its numerical solution, including a methodology
for solving the inverse problem of finding the model parameters that best match
empirical data. Using this methodology, we compare the steady-state solutions
of the Fokker-Planck equation with data from the United States Survey of
Consumer Finances over a time period of 27 years. In doing so, we demonstrate
agreement with empirical data of an average error less than 0.16\% over this
time period. We present the model parameters for the US wealth distribution
data as a function of time under the assumption that the distribution responds
to their variation adiabatically. We argue that the time series of model
parameters thus obtained provides a valuable new diagnostic tool for analyzing
wealth inequality.
