We provide a general framework for analysing multi-dimensional portfolio liquidation problems with instantaneous and persistent price impact and stochastic resilience. We show that the value function can be described by a system of multi-dimensional backward stochastic Riccati differential equations (BSRDEs) with a singular terminal condition. We prove the existence of a solution to the BSRDE system and characterise both the value function and the optimal strategy in terms of that solution. We prove that the solution to the liquidation problem can be approximated by the solutions to a sequence of unconstrained problems with increasing penalisation of open positions at the terminal time. Our proof is based on a novel a priori estimate for the approximating BSRDE systems, from which we infer the convergence of the optimal trading strategies for the unconstrained models to an admissible liquidation strategy for the original problem.

中文翻译：

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随机弹性下的多维最优交易执行

我们提供了一个通用框架，用于分析具有瞬时和持续价格影响以及随机弹性的多维投资组合清算问题。我们表明，可以通过具有奇异终端条件的多维反向随机Riccati微分方程（BSRDE）系统来描述值函数。我们证明了BSRDE系统解决方案的存在，并根据该解决方案表征了价值函数和最优策略。我们证明，对于清算问题的解决方案可以通过对一系列无约束问题的解决方案进行近似估算，这些解决方案随着在终端时间对未平仓头寸的惩罚增加。我们的证明基于近似BSRDE系统的新颖先验估计，