Asynchronous stochastic price pump

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.

我们提出了一个在一群主体中进行股票交易的模型，其中每个主体的行为是为了实现其目标股票与债券的比率，并且作为一种反馈机制，遵循一种市场自适应策略。在这个模型中，在一个交易期间只有一部分主体参与买卖股票，而群体中的其余主体接受新设定的价格。通过数值模拟，我们表明随机过程在收益方面稳定在一个平稳状态。平均收益可能大于或小于债券收益，并且它由自适应机制的参数决定。当相互作用的主体数量固定时，收益的分布遵循对数正态密度。在这种情况下，我们根据主体风险水平的变化率给出了平均收益率的解析公式，并通过数值模拟对该公式进行了验证。然而，当每个时期相互作用的主体数量是随机的时，收益的分布可能会显著偏离对数正态分布，特别是当相互作用主体数量分布的方差增加时。