Title: Asynchronous stochastic price pump,
Abstract: We propose a model for equity trading in a population of agents where each
agent acts to achieve his or her target stock-to-bond ratio, and, as a feedback
mechanism, follows a market adaptive strategy. In this model only a fraction of
agents participates in buying and selling stock during a trading period, while
the rest of the group accepts the newly set price. Using numerical simulations
we show that the stochastic process settles on a stationary regime for the
returns. The mean return can be greater or less than the return on the bond and
it is determined by the parameters of the adaptive mechanism. When the number
of interacting agents is fixed, the distribution of the returns follows the
log-normal density. In this case, we give an analytic formula for the mean rate
of return in terms of the rate of change of agents' risk levels and confirm the
formula by numerical simulations. However, when the number of interacting
agents per period is random, the distribution of returns can significantly
deviate from the log-normal, especially as the variance of the distribution for
the number of interacting agents increases.