论文标题
从银行和债务的美元交换模型中揭示了两阶段的动态
Uncovering a two-phase dynamics from a dollar exchange model with bank and debt
论文作者
论文摘要
我们调查了具有集体债务限制的货币交易模型：代理商在彼此之间将一美元随机捐赠，只要他们至少拥有一美元，或者如果银行没有空的，他们可以从中央银行借一美元。令人惊讶的是，这种动态最终导致财富的不对称拉普拉斯分布（在[22]中猜想，并在最近的一项工作[18]中正式显示）。在此手稿中，我们执行了正式的平均场限制，因为代理的数量进入了无限，我们发现了两相（ODE）动力学。还显示了在较大的时间限制中与独特平衡（双面几何）分布的融合，银行的作用和债务的作用（就Gini指数或财富不平等而言）也将在数值上进行探索。
We investigate the unbiased model for money exchanges with collective debt limit: agents give at random time a dollar to one another as long as they have at least one dollar or they can borrow a dollar from a central bank if the bank is not empty. Surprisingly, this dynamics eventually leads to an asymmetric Laplace distribution of wealth (conjectured in [22] and shown formally in a recent work [18]). In this manuscript, we carry out a formal mean-field limit as the number of agents goes to infinity where we uncover a two-phase (ODE) dynamics. Convergence towards the unique equilibrium (two-sided geometric) distribution in the large time limit is also shown and the role played by the bank and debt (in terms of Gini index or wealth inequality) will be explored numerically as well.
