论文标题
带有噪音的平均场地游戏价格模型
A mean-field game price model with noise
论文作者
论文摘要
在本文中，我们提出了一种平均场景模型，以构成商品的价格形成，该商品的产量会受到随机波动的影响。该模型概括了现有的确定性价格形成模型。代理商试图通过以供求之间的平衡为特征的价格选择其交易率来最大程度地降低其平均成本。假定供应和价格过程遵循随机微分方程。在这里，我们表明，对于线性动态和二次成本，最佳交易率是以反馈形式确定的。因此，价格是作为随机微分方程的解决方案而产生的，其系数取决于普通微分方程系统的解决方案。
In this paper, we propose a mean-field game model for the price formation of a commodity whose production is subjected to random fluctuations. The model generalizes existing deterministic price formation models. Agents seek to minimize their average cost by choosing their trading rates with a price that is characterized by a balance between supply and demand. The supply and the price processes are assumed to follow stochastic differential equations. Here, we show that, for linear dynamics and quadratic costs, the optimal trading rates are determined in feedback form. Hence, the price arises as the solution to a stochastic differential equation, whose coefficients depend on the solution of a system of ordinary differential equations.
