两阶段金融衍生品清算问题的半定规划松弛方法  

The semi-definite programming relaxation method for two-period financial derivatives'liquidation problem

作　　者：李叶 洪陈春[2] 罗和治 LI Ye;HONG Chenchun;LUO Hezhi(School of Science,Zhejiang Sci-Tech University,Hangzhou 310018,China;Huaxin Consulting Co.,Ltd.,Hangzhou 310014,China)

机构地区：[1]浙江理工大学理学院,杭州310018 [2]华信咨询设计研究院有限公司,杭州310014

出　　处：《浙江理工大学学报（自然科学版）》2024年第4期566-572,共7页Journal of Zhejiang Sci-Tech University(Natural Sciences)

基　　金：国家自然科学基金项目(12271485,11871433);浙江省自然科学基金项目(LZ21A010003)。

摘　　要：在不限制暂时性及永久性价格影响参数大小关系下,研究两阶段金融衍生品清算问题的半定规划(Semi-definite programming,SDP)松弛方法,其优化模型为一个带有线性和单个非凸二次约束的非凸二次规划(Quadratically constrained quadratic program,QCQP)问题。针对该非凸QCQP问题,给出了一个带有Secant割的SDP松弛,并估计了它与原问题之间的间隙。随机例子的数值结果表明该SDP松弛可以得到原问题更紧的上界,从而为寻求原问题的一个好的近似解提供方法。The semi-definite programming(SDP)relaxation method for two-period financial derivatives′liquidation problem is studied without restricting the relationship between the magnitude of the temporary and permanent price impact parameters,and the optimization model is a nonconvex quadratically constrained quadratic programming(QCQP)problem with linear and single nonconvex quadratic constraints.An SDP relaxation with secant cuts for this nonconvex QCQP problem is presented and the gap between it and the original problem is estimated.The numerical results of random instances show that the SDP relaxation can obtain a tighter upper bound to the original problem and then provides a method for finding a good approximate solution to the problem.

关 键 词：两阶段清算模型 金融衍生品 非凸二次规划 SDP松弛 Secant割 

分 类 号：O224[理学—运筹学与控制论]