投资组合最优清算问题的双层规划模型

doi:10.15960/j.cnki.issn.1007-6093.2026.03.003

运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (3): 41-55.doi: 10.15960/j.cnki.issn.1007-6093.2026.03.003

所属专题：运筹与管理前沿：模型、算法及其应用专辑

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投资组合最优清算问题的双层规划模型

李雪鹏¹, 徐凤敏^2†

1. 西安财经大学数学学院, 陕西西安 710100;
2. 西安交通大学经济与金融学院, 陕西西安 710061

收稿日期:2026-06-25 发布日期:2026-09-12
通讯作者: 徐凤敏 E-mail:fengminxu@mail.xjtu.edu.cn
基金资助:
国家自然科学基金(No.12471297)

A bilevel programming model for optimal portfolio liquidation problem

LI Xuepeng¹, XU Fengmin^2†

1. School of Mathematics, Xi'an University of Finance and Economics, Xi'an 710100, Shaanxi, China;
2. School of Economics and Finance, Xi'an Jiaotong University, Xi'an 710061, Shaanxi, China

Received:2026-06-25 Published:2026-09-12

摘要/Abstract

摘要： 针对传统最优清算模型忽视策略互动的局限,本文构建投资组合清算的双层规划模型,刻画领导者和跟随者依次交易的价格博弈过程。理论分析给出跟随者最优策略的显式刻画,证明现金约束在最优解处取等式,并量化领导者因跟随者交易承担的额外损失。针对模型的非凸嵌套结构,设计混合量子粒子群算法求解。数值实验表明,弱势地位的领导者倾向于提前清空相关资产以规避跟随者引发的价格下跌;若忽视博弈机制,领导者相对损失最高可达46.6%。

关键词: 最优清算, 双层规划, 凸QCQP, 金融优化, 投资组合

Abstract: To address the limitation of traditional optimal portfolio liquidation models that overlook strategic interactions, this paper develops a bilevel programming model for portfolio liquidation, characterizing the sequential trading game between a leader and a follower. Theoretical analysis explicitly characterizes the follower's optimal strategy, proves that the cash constraint is active at the optimum, and quantifies the leader's additional loss caused by the follower's trading. A hybrid quantum-behaved particle swarm optimization algorithm is designed to solve the nonconvex nested model. Numerical experiments show that a disadvantaged leader tends to preemptively liquidate vulnerable assets to avoid price declines triggered by the follower; ignoring the game mechanism can result in a relative loss of up to 46.6%.

Key words: optimal liquidation, bilevel programming, convex QCQP, financial optimization, portfolio management

中图分类号:

O224

李雪鹏, 徐凤敏. 投资组合最优清算问题的双层规划模型[J]. 运筹学学报（中英文）, 2026, 30(3): 41-55.

LI Xuepeng, XU Fengmin. A bilevel programming model for optimal portfolio liquidation problem[J]. Operations Research Transactions, 2026, 30(3): 41-55.

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投资组合最优清算问题的双层规划模型

A bilevel programming model for optimal portfolio liquidation problem

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