| 求解带有交易费的CVaR投资组合模型的L-S算法 |
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| 引用本文： | 张茂军,南江霞,高爱华.求解带有交易费的CVaR投资组合模型的L-S算法[J].经济数学,2012,29(2):73-78. |
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| 作者姓名： | 张茂军 南江霞 高爱华 |
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| 作者单位： | 1. 桂林电子科技大学数学与计算科学学院,广西桂林,541004
2. 大连理工大学数学科学学院,辽宁大连,116024 |
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| 基金项目： | 国家自然科学基金资助项目，桂林电子科技大学博士启动基金，广西教育厅项目，广西自然科学基金资助项目 |
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| 摘 要： | 本文假设投资者是风险厌恶型,用CVaR作为测量投资组合风险的方法.在预算约束的条件下,以最小化CVaR为目标函数,建立了带有交易费用的投资组合模型.将模型转化为两阶段补偿随机优化模型,构造了求解模型的随机L-S算法.为了验证算法的有效性,用中国证券市场中的股票进行数值试验,得到了最优投资组合、VaR和CVaR的值.而且对比分析了有交易费和没有交易费的最优投资组合的不同,给出了相应的有效前沿.
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| 关 键 词： | CVaR 投资组合 交易费 L-S算法 二阶段补偿优化 |
L-S Algorithm for the CVaR Portfolio Models with Transaction Costs |
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| ZHANG Mao-jun,NAN Jiang-xi,GAO Ai-hua.L-S Algorithm for the CVaR Portfolio Models with Transaction Costs[J].Mathematics in Economics,2012,29(2):73-78. |
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| Authors: | ZHANG Mao-jun NAN Jiang-xi GAO Ai-hua |
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| Institution: | 1.School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guangxi,Guilin 541004,China;2.School of Mathematics Science,Dalian University of Technology,Liaoning,Dalian 116024,China) |
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| Abstract: | Assuming that investors are risk averse,CVaR was used as a method to measure a portfolio risk.A portfolio model with transaction costs was constructed under the budget constraint condition and minimizing the CVaR as an objective function.The model was transformed into a two-stage recourse problem of stochastic programming,and a stochastic L-S algorithm was designed to solve the model.The efficiency of our algorithm was illustrated by a portfolio selection experiment on the China market,and the optimal portfolio,VaR and CVaR were obtained.Moreover,the differences between the optimal portfolio with transaction costs and the one with no transaction costs were analyzed,and the corresponding efficient frontiers were given. |
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| Keywords: | CVaR portfolio transaction cost L-S algorithm two-stage recourse optimization |
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