Asynchronous stochastic price pump

TL;DR

This paper introduces a stochastic model for equity trading with adaptive agents, analyzing how partial participation influences return distributions and deriving formulas for mean returns under different interaction scenarios.

Contribution

It presents a novel model of asynchronous trading with adaptive feedback, providing analytical and numerical insights into return distributions and their dependence on agent participation.

Findings

Returns follow a log-normal distribution when the number of interacting agents is fixed.

The mean return depends on the adaptive mechanism parameters.

Variable agent participation can lead to deviations from log-normal return distributions.

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.