SIAM Journal on Financial Mathematics, Volume 11, Issue 1, Page 1-26, January 2020.
We study Nash equilibria for inventory-averse high-frequency traders (HFTs), who trade to exploit information about future price changes. For discrete trading rounds, the HFTs' optimal trading strategies and their equilibrium price impact are described by a system of nonlinear equations; explicit solutions are obtained around the high-frequency limit. Unlike in the risk-neutral case, the optimal inventories become mean-reverting and vanish as the number of trading rounds becomes large. In contrast, the HFTs' risk-adjusted profits and the equilibrium price impact converge to their risk-neutral counterparts. Compared to cooperative HFTs, Nash competition leads to excess trading, so that marginal transaction taxes in fact decrease market liquidity.

中文翻译：

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竞争不完善的高频交易库存管理

SIAM金融数学杂志，第11卷，第1期，第1-26页，2020年1月。
我们为厌恶存货的高频交易者（HFT）研究纳什均衡，他们进行交易以利用有关未来价格变化的信息。对于离散的交易回合，HFT的最佳交易策略及其均衡价格影响通过非线性方程式系统描述。在高频极限附近获得显式解。与在风险中立的情况下不同，随着交易回合的数量变大，最优库存变得平均且消失。相比之下，高频交易的风险调整后利润和均衡价格的影响收敛至风险中性的对手。与合作式高频交易相比，纳什竞争导致过多的交易，因此边际交易税实际上减少了市场流动性。