【廿周年院庆学术报告122】· 【和山数学论坛第397期】
一、报告题目：Effective Algorithms for Optimal Portfolio Deleveraging Problem with Cross Impact
二、报告人：罗和治教授
三、时间：2023年12月29日(周五)上午9:00-10:00
四、地点：闻理园A3-217
报告摘要：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 $\epsilon$-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 real data and randomly generated medium- and large-scale OPD instances.
报告人简介：罗和治，博士，浙江理工大学特聘教授，浙江省“151人才工程”第二层次入选者。现任中国运筹学会理事,中国运筹学会数学规划分会常务理事。2007年获上海大学运筹学专业博士学位，2008-2010年在复旦大学管理科学与工程专业从事博士后研究，2011年和2013年在美国伊利诺伊大学香槟分校做访问学者。主要研究方向为全局最优化理论与算法及其在金融工程中的应用。已在国际运筹与优化权威期刊SIAM Journal on Optimization、Mathematical Programming Computation、INFORMS Journal on Computing、Mathematical Finance、Computational Optimization and Applications、Journal of Global Optimization、Journal of Optimization Theory and Applications等上发表SCI论文30余篇。主持了国家自然科学基金面上项目4 项，国家自然科学基金区域创新联合基金重点项目子课题1项，中国博士后科学基金特别资助项目1 项，浙江省自然科学基金重点项目1项和面上项目3项。曾获中国运筹学会青年科技奖提名奖（2010）、浙江省自然科学学术奖三等奖(2012)。
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