论文标题
具有交叉影响的最佳投资组合去杠杆化问题的有效算法
Effective Algorithms for Optimal Portfolio Deleveraging Problem with Cross Impact
论文作者
论文摘要
我们研究了永久性和临时价格影响的最佳投资组合交易（OPD）问题，目的是在满足规定的债务/权益要求的同时最大化股权。我们考虑了不同资产之间的交叉影响的真实情况。然而，最终的问题是一个具有二次约束和盒子约束的非凸二次程序，已知是NP-HARD。在本文中，我们首先开发了一种连续的凸优化（SCO）方法来解决OPD问题，并表明SCO算法会收敛到其转换问题的KKT点。其次，我们为OPD问题提出了一种有效的全局算法，该算法集成了SCO方法，简单的凸松弛和一个分支结合的框架，以识别预先指定的$ε$ -TOLERANCE中OPD问题的全局最佳解决方案。我们建立了算法的全球融合并估计其复杂性。我们还进行了数值实验，以证明使用真实数据以及随机生成的中等和大规模OPD问题实例的我们提出的算法的有效性。
We investigate the optimal portfolio deleveraging (OPD) problem with permanent and temporary price impacts, where the objective is to maximize equity while meeting a prescribed debt/equity requirement. We take the real situation with cross impact among different assets into consideration. The resulting problem is, however, a non-convex quadratic program with a quadratic constraint and a box constraint, which is known to be NP-hard. In this paper, we first develop a successive convex optimization (SCO) approach for solving the OPD problem and show that the SCO algorithm converges to a KKT point of its transformed problem. Second, we propose an effective global algorithm for the OPD problem, which integrates the SCO method, simple convex relaxation and a branch-and-bound framework, to identify a global optimal solution to the OPD problem within a pre-specified $ε$-tolerance. We establish the global convergence of our algorithm and estimate its complexity. We also conduct numerical experiments to demonstrate the effectiveness of our proposed algorithms with both the real data and the randomly generated medium- and large-scale OPD problem instances.
