论文标题
多资产和多代理市场影响游戏的不稳定性
Instabilities in Multi-Asset and Multi-Agent Market Impact Games
论文作者
论文摘要
我们考虑了一组代理商在存在瞬态价格影响和额外二次交易成本的情况下交易资产组合的一般问题，我们通过分析和数值方法研究了纳什均衡。 Schied＆Zhang（2019）和Luo＆Schied（2020）的框架显着扩展了，他们考虑了单一资产案例，我们证明了相关均值变化优化问题的相应NASH平衡的存在和唯一性。然后，我们将注意力集中在模型参数上的条件上，这使代理商以平衡的态度的交易概况，因此价格轨迹，非常振荡和市场不稳定。尽管Schied＆Zhang（2019）和Luo＆Schied（2020）强调了交易成本价值在确定稳定阶段和不稳定阶段之间的过渡中的重要性，但我们表明，市场对代理商数量的影响以及资产的数量以及资产的数量以及M的资产数量确定了市场的稳定性（在J中的J和M）。
We consider the general problem of a set of agents trading a portfolio of assets in the presence of transient price impact and additional quadratic transaction costs and we study, with analytical and numerical methods, the resulting Nash equilibria. Extending significantly the framework of Schied & Zhang (2019) and Luo & Schied (2020), who considered the single asset case, we prove the existence and uniqueness of the corresponding Nash equilibria for the related mean-variance optimization problem. We then focus our attention on the conditions on the model parameters making the trading profile of the agents at equilibrium, and as a consequence the price trajectory, wildly oscillating and the market unstable. While Schied & Zhang (2019) and Luo & Schied (2020) highlighted the importance of the value of transaction cost in determining the transition between a stable and an unstable phase, we show that also the scaling of market impact with the number of agents J and the number of assets M determines the asymptotic stability (in J and M ) of markets.
