Performance evaluation of portfolios with fuzzy returns
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1581-1600.

The existing literature on DEA (Data Envelopment Analysis) for evaluating fuzzy portfolios usually takes risk as an input and return as an output. This assumption is actually not congruent with the real investment process, where the input is the initial wealth and the output is the corresponding terminal wealth. As for the risk and return, which are essentially two indicators derived from the terminal wealth, both should be regarded as outputs. In addition, few studies have employed the diversification model (nonlinear DEA) to estimate the fuzzy portfolio efficiency (PE), despite the fact that there are many studies available within the framework of classical probability theory. Further, the relationship between DEA and diversification models needs to be defined. In this paper, we take the initial wealth as an input, while the return and risk of terminal wealth are taken as desirable and undesirable outputs, respectively. We construct different evaluation models under the fuzzy portfolio framework. The relationships among the evaluation model based on a real frontier, the diversification model and the DEA model are investigated. We show the convergence of the diversification and DEA models under the fuzzy theory framework. Some simulations as well as empirical analysis are presented to further verify the effectiveness of the proposed models. Finally, we check the robustness of the evaluation results by using the bootstrap re-sampling approach.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2019071
Classification : 90B30, 90B50, 90C05, 90C30, 90C70
Mots-clés : Fuzzy portfolio evaluation, possibilistic measures, diversification model, DEA, bootstrap re-sampling
Zhou, Zhongbao 1 ; Chen, Enming 1 ; Xiao, Helu 1 ; Ren, Tiantian 1 ; Jin, Qianying 1

1 
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     author = {Zhou, Zhongbao and Chen, Enming and Xiao, Helu and Ren, Tiantian and Jin, Qianying},
     title = {Performance evaluation of portfolios with fuzzy returns},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1581--1600},
     publisher = {EDP-Sciences},
     volume = {53},
     number = {5},
     year = {2019},
     doi = {10.1051/ro/2019071},
     mrnumber = {4016080},
     zbl = {1431.90060},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2019071/}
}
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Zhou, Zhongbao; Chen, Enming; Xiao, Helu; Ren, Tiantian; Jin, Qianying. Performance evaluation of portfolios with fuzzy returns. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1581-1600. doi : 10.1051/ro/2019071. http://archive.numdam.org/articles/10.1051/ro/2019071/

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