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%。
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%.
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