论文标题
关于最佳交易的有限人口游戏
On finite population games of optimal trading
论文作者
论文摘要
我们研究了包括有限人口的最佳交易的随机差异游戏。当前框架中有市场摩擦，采用随机永久性和临时价格影响的形式。此外，贸易商之间的信息是不对称的，具有温和的假设。对于恒定的市场参数，我们提供专门的结果。每个玩家不仅基于她的信息级别，而且基于她的特定喜好选择她的参数。工作的第一部分是我们检查不受约束的问题的地方，在该问题中，交易者不一定必须通过消失的库存到达地平线的尽头。在续集中，我们开始分析受约束的情况作为上一个前一个的渐近极限。在合适的假设下，我们证明了两个框架中NASH平衡的存在和独特性。我们通过将基本模型扩展到分层市场的扩展来结束，为此我们确定了stackelberg-nash平衡的存在，独特性和表征。
We investigate stochastic differential games of optimal trading comprising a finite population. There are market frictions in the present framework, which take the form of stochastic permanent and temporary price impacts. Moreover, information is asymmetric among the traders, with mild assumptions. For constant market parameters, we provide specialized results. Each player selects her parameters based not only on her informational level but also on her particular preferences. The first part of the work is where we examine the unconstrained problem, in which traders do not necessarily have to reach the end of the horizon with vanishing inventory. In the sequel, we proceed to analyze the constrained situation as an asymptotic limit of the previous one. We prove the existence and uniqueness of a Nash equilibrium in both frameworks, alongside a characterization, under suitable assumptions. We conclude the paper by presenting an extension of the basic model to a hierarchical market, for which we establish the existence, uniqueness, and characterization of a Stackelberg-Nash equilibrium.
