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BIMSA Digital Economy Lab Seminar
High-order Moment Portfolio Optimization via An Accelerated Difference-of-Convex Programming Approach and Sum-of-Square Theory
High-order Moment Portfolio Optimization via An Accelerated Difference-of-Convex Programming Approach and Sum-of-Square Theory
演讲者
时间
2025年01月06日 15:20 至 16:20
地点
A3-2-303
线上
Zoom 230 432 7880
(BIMSA)
摘要
The Mean-Variance-Skewness-Kurtosis (MVSK) high-order moment portfolio optimization model is a nonconvex quartic polynomial minimization problem over a standard simplex. This problem can be formulated as a Difference-of-Convex (DC) program. To tackle this, we propose a novel DC formulation for the MVSK model based on the Difference-of-Convex-Sums-of-Squares (DC-SOS). The classical DCA algorithm is applied to solve this formulation, and we further develop an accelerated version, Boosted DCA (BDCA), designed for general DC programs with convex constraints. The acceleration of BDCA is achieved through a line search strategy, such as an Armijo-type inexact line search, along the DC descent direction based on consecutive DCA iterations. We provide rigorous convergence analysis to establish the theoretical foundation of BDCA. Two decomposition approaches, DC-SOS and projective DC decomposition, are tested, demonstrating the versatility of the method.
Numerical simulations using both synthetic and real-world portfolio datasets validate the effectiveness of BDCA. The method is benchmarked against solvers like KNITRO, FILTERSD, IPOPT, and MATLAB fmincon, showcasing superior computational efficiency and robustness. Notably, the DC-SOS decomposition provides a better convex over-approximation for polynomials, significantly reducing the number of iterations required for DCA and BDCA. BDCA consistently achieves the best numerical results with fewer iterations compared to the classical DCA. The BDCA method proves to be an advanced and practical tool for high-order moment portfolio optimization. Its enhanced convergence rates and improved solution quality highlight its applicability in solving complex portfolio optimization problems effectively.
演讲者介绍
Yajuan Wang is a postdoctoral researcher in Strategic Management at the School of Management, Fudan University, and an intern at BIMSA. She earned her Ph.D. in Strategic Management from Shanghai University of Finance and Economics. Her research interests span strategic management, human resources, and finance, with a focus on dynamic competition, corporate innovation, top management teams (TMT), talent resource development, venture capital and portfolio investment.