Abstract：This talk is about a chance constrained program where the randomness takes a quadratic form of random variables following multivariate Gaussian mixture distribution (GMD). It is proved that the asymptotic distribution of this kind of quadratic randomness is a univariate GMD under some mild conditions. Furthermore, by restricting the condition numbers of covariance matrices associated with the Gaussian components of the multivariate GMD, the approximating error can be reduced effectively. These findings help to translate this type of chance constrained program into a more tractable one for searching global optimal solutions. For the case where the quadratic randomness is expressed in a linear form of the decision variables, if the confidence level is required sufficiently high, solutions feasible to the chance constraint usually constitute a convex set, indicating that solving the problem is actually easy. Otherwise, for case without convexity at relatively low confidence level, an existing branch-and-bound algorithm that fits the special structure of this problem can be used to search the global optimal solutions. An illustrative application to the VaR optimization of nonlinear portfolio is conducted to verify the effectiveness of this unified approach.

报告人简介：朱书尚，湖南人，本科（1997）和硕士（2000）毕业于湘潭大学， 2003年毕业于中国科学院系统科学研究所，获管理学博士学位。2003年7月到2012年1月于复旦大学管理学院任教。2012年1月，以“百人计划”引进人才身份加入中山大学，现任中山大学管理学院财务与投资系教授/博士生导师。多次到香港中文大学、京都大学做访问交流。长期从事金融工程与风险管理研究。当前研究兴趣主要包括投资组合优化、Forward-Looking收益预测、风险值优化、系统性风险传染机制与测度等。在国内外专业学术期刊上发表论文70余篇，其中包括在Operations Research, INFORMS Journal on Computing, Mathematical Finance, IEEE Transactions on Automatic Control, IISE Transactions, Journal of Economic Dynamics and Control, Journal of Banking and Finance, Journal of Financial Stability, Quantitative Finance, Journal of Computational Finance,《管理科学学报》和《金融研究》等期刊上发表的多篇论文。现任中国运筹学会常务理事、中国运筹学会金融工程与金融风险管理分会副理事长；广东经济学会副会长；中国系统工程学会金融系统工程专业委员会委员等职。现任国际期刊 Journal of the Operations Research Society of China和Humanities and Social Sciences Communications编委。