论文标题
使用半明星策略的最佳投资组合清算的平均场地控制问题
A Mean-Field Control Problem of Optimal Portfolio Liquidation with Semimartingale Strategies
论文作者
论文摘要
我们考虑了Càdlàg半明星策略的平均场控制问题，该策略在具有瞬态市场影响和自我激发顺序的投资组合清算模型中产生。我们表明，价值函数仅通过其定律取决于状态过程，并且其系数是线性界面形式，并且其系数满足了非标准riccati-type方程的耦合系统。 Riccati方程是通过从一系列离散时间模型传递到连续的时间限制来启发的。复杂的转换表明，该系统可以将其转化为标准的Riccati形式，从中我们推断出全球解决方案的存在。我们的分析表明，最佳策略仅在交易期开始和结束时跳跃。
We consider a mean-field control problem with càdlàg semimartingale strategies arising in portfolio liquidation models with transient market impact and self-exciting order flow. We show that the value function depends on the state process only through its law, and that it is of linear-quadratic form and that its coefficients satisfy a coupled system of non-standard Riccati-type equations. The Riccati equations are obtained heuristically by passing to the continuous-time limit from a sequence of discrete-time models. A sophisticated transformation shows that the system can be brought into standard Riccati form from which we deduce the existence of a global solution. Our analysis shows that the optimal strategy jumps only at the beginning and the end of the trading period.
