论文标题
带有自振订单流量的投资组合清算游戏
Portfolio Liquidation Games with Self-Exciting Order Flow
论文作者
论文摘要
我们通过自动订单流量分析新型投资组合清算游戏。都考虑了N-Glayer游戏和均值比赛。我们假设玩家的交易活动会影响未来市场订单的动态，从而产生额外的瞬态价格影响。鉴于她的竞争对手的策略，每个玩家都解决了均值场控制问题。我们在两款游戏中以未知终端状态的新型平均FBSDE系统来表征开环NASH平衡。在弱相互作用条件下，我们证明了FBSDE系统具有独特的解决方案。使用不需要成本函数的新型最大原理，我们最终证明了FBSDE系统的解决方案确实确实提供了开环Nash Equilibria的存在和独特性。
We analyze novel portfolio liquidation games with self-exciting order flow. Both the N-player game and the mean-field game are considered. We assume that players' trading activities have an impact on the dynamics of future market order arrivals thereby generating an additional transient price impact. Given the strategies of her competitors each player solves a mean-field control problem. We characterize open-loop Nash equilibria in both games in terms of a novel mean-field FBSDE system with unknown terminal condition. Under a weak interaction condition we prove that the FBSDE systems have unique solutions. Using a novel sufficient maximum principle that does not require convexity of the cost function we finally prove that the solution of the FBSDE systems do indeed provide existence and uniqueness of open-loop Nash equilibria.
