English

运筹学学报（中英文） ›› 2026, Vol. 30 ›› Issue (1): 108-120.doi: 10.15960/j.cnki.issn.1007-6093.2026.01.007

• • 上一篇    

两阶段金融衍生品清算问题的一个快速SDP松弛

黄印1, 罗和治2,†   

  1. 1. 浙江理工大学理学院, 浙江杭州 310018;
    2. 浙江师范大学数学科学学院, 浙江金华 321004
  • 收稿日期:2024-02-04 发布日期:2026-03-16
  • 通讯作者: 罗和治 E-mail:hzluo@zstu.edu.cn
  • 基金资助:
    国家自然科学基金 (No. 12271485)

A faster SDP relaxation for two-period financial derivatives liquidation problem

HUANG Yin1, LUO Hezhi2,†   

  1. 1. College of Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, Zhejiang, China;
    2. School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
  • Received:2024-02-04 Published:2026-03-16

PDF

1

摘要： 本文在没有凸性假设下考虑两阶段金融衍生品清算问题, 其优化模型为NP-难的带单个非凸二次约束和线性约束的非凸二次规划问题。针对该模型的特殊结构, 构造了一个快速的新半定规划(semi-definite programming, SDP)松弛, 估计了它与原问题之间的间隙, 并证明了它比文献中已有SDP松弛提供更紧的下界。数值实验表明该SDP松弛能快速得到原问题的一个非常紧的下界, 为设计求解原问题全局最优解的分支定界算法提供有效的下界。

关键词: 金融优化, 两阶段金融衍生品清算问题, 非凸QCQP, SDP松弛

Abstract: In this paper, we consider a two-period financial derivative liquidation problem without the convexity assumption. Its optimization model is a non-convex quadratic programming problem with a single quadratic constraint and linear constraints, which is NP-hard. We propose a faster new semi-definite programming (SDP) relaxation for this model by making use of its special structure, and estimate the gap between it and the original problem. We also show that it provides a tighter lower bound than the existing SDP relaxation in the literature. Numerical experiments show that this SDP relaxation can fast provide a very tight lower bound for the original problem, thus can provide effective lower bounds in branch-and-bound algorithm to find the global optimal solution of the problem.

Key words: financial optimization, two-period financial derivative liquidation problem, non-convex QCQP, SDP relaxation

中图分类号: