Mean-CVaR portfolio selection: A nonparametric estimation framework

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• 作者：Haixiang Yao^a ; ^{yaohaixiang@gdufs.edu.cn} ; Zhongfei Li^b ; ^c ; ^{lnslzf@mail.sysu.edu.cn} ; Yongzeng Lai^d ; ^ylai@wlu.ca
• 关键词：Portfolio selection ; Conditional Value-at-Risk ; Nonparametric estimation ; Convex optimization ; Monte Carlo simulation
• 刊名：Computers and Operations Research
• 出版年：2013
• 出版时间：April, 2013
• 年：2013
• 卷：40
• 期：4
• 页码：1014-1022
• 全文大小：343 K

文摘

In this paper, we use Conditional Value-at-Risk (CVaR) to measure risk and adopt the methodology of nonparametric estimation to explore the mean-CVaR portfolio selection problem. First, we obtain the estimated calculation formula of CVaR by using the nonparametric estimation of the density of the loss function, and formulate two nonparametric mean-CVaR portfolio selection models based on two methods of bandwidth selection. Second, in both cases when short-selling is allowed and forbidden, we prove that the two nonparametric mean-CVaR models are convex optimization problems. Third, we show that when CVaR is solved for, the corresponding VaR can also be obtained as a by-product. Finally, we present a numerical example with Monte Carlo simulations to demonstrate the usefulness and effectiveness of our results, and compare our nonparametric method with the popular linear programming method.