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Mathematics
Article . 2026 . Peer-reviewed
License: CC BY
Data sources: Crossref
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On Intensively Criticizing and Envisioning the Research on Multiple-Objective Portfolio Selection from the Perspective of Capital Asset Pricing Models

Authors: Yue Qi; Jianing Huang; Yixuan Zhu;

On Intensively Criticizing and Envisioning the Research on Multiple-Objective Portfolio Selection from the Perspective of Capital Asset Pricing Models

Abstract

Nobel Laureate Markowitz originates portfolio selection as the birth of modern finance. Nobel Laureate Sharpe implements portfolio selection and originates capital asset pricing models. Nobel Laureate Fama also implements portfolio selection and originates zero-covariance capital asset pricing models. After these feats, researchers have gradually realized additional objectives and have promisingly extended portfolio selection into multiple-objective portfolio selection. However, there hardly exists research to leap from multiple-objective portfolio selection to multiple-objective capital asset pricing models (as initiated by Markowitz and Sharpe in finance). Moreover, the extension is basically confined to the branches of mathematics, operations research, optimization, and computer sciences. Many researchers sufficiently review multiple-objective portfolio selection. However, the reviews are extensive. Instead, we intensively criticize and envision the research on multiple-objective portfolio selection from the perspective of capital asset pricing models by crystallizing the research limitations and heralding future directions. Specifically, we emphasize seven research limitations for multiple-objective portfolio optimization, multiple-objective capital asset pricing models, and multiple-objective zero-covariance capital asset pricing models. We also generalize from common three-objective portfolio selection to k-objective portfolio selection. Visually, we orchestrate figures to delineate the complexity. Theoretically, this paper heralds challenging but encouraging future directions. Pragmatically, this paper proposes a formulation for the multiple-objective nature of practical convolution in finance.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Top 10%
Average
Average
gold