基于DC规划的多期风险价值约束投资组合优化
Multi-period Value-at-Risk Constrained Portfolio Optimization via DC Programming
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- University of Economics Ho Chi Minh City（胡志明市经济大学）
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中文总结 AI 辅助
该研究针对带VaR约束等的多期投资组合优化问题，提出iBDCA算法求解，经理论分析与数值实验验证其有效性，可平衡收益、风险等多维度指标。
中文摘要 AI 辅助
我们研究了带有限情景风险价值（VaR）约束、交易成本及多样化正则化的多期投资组合优化问题。利用有限情景下的VaR-CVaR恒等式，我们在基础凸投资组合集上推导出惩罚型凸差（DC）形式。为求解该非光滑非凸问题，我们提出了投影惯性增强凸差函数算法（iBDCA），该算法结合了惯性外推、目标保护及增强线搜索。我们证明该方法定义明确，生成的目标序列单调递减，且对惩罚型DC问题仅存在临界点聚点。在聚点处的局部无并列条件下，我们进一步建立了全序列收敛性及局部R-线性速率。数值实验在匹配的问题实例上将iBDCA与DCA及标准BDCA进行了比较；样本外回测还加入了等权重和买入持有基准，以说明已实现收益、风险、交易成本及经验VaR控制之间的权衡关系。
英文摘要
We study a multi-period portfolio optimization problem with finite-scenario Value-at-Risk (VaR) constraints, transaction costs, and diversification regularization. Using a finite-scenario VaR--CVaR identity, we derive a penalized difference-of-convex (DC) formulation over the underlying convex portfolio set. To solve the resulting nonsmooth and nonconvex problem, we propose a projected inertial Boosted Difference-of-Convex Functions Algorithm (iBDCA) that combines inertial extrapolation, an objective safeguard, and a boosted line search. We prove that the method is well defined, generates a monotonically decreasing objective sequence, and has only critical accumulation points for the penalized DC problem. Under a local no-ties condition at an accumulation point, we further establish whole sequence convergence with a local \(R\)-linear rate. Numerical experiments compare iBDCA with DCA and standard BDCA on matched problem instances. Out-of-sample backtests additionally include equal-weight and buy-and-hold benchmarks to illustrate the trade-offs among realized return, risk, transaction costs, and empirical VaR control.
