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Portfolio optimization under a minimax rule revisited
Optimization ( IF 2.2 ) Pub Date : 2021-05-29 , DOI: 10.1080/02331934.2021.1928665
Kaiwen Meng 1 , Hongyu Yang 1 , Xiaoqi Yang 2 , Carisa Kwok Wai Yu 3
Affiliation  

In this paper, we revisit the bi-criteria portfolio optimization model where the short selling is permitted, and a trade-off is sought between the expected return rate of a portfolio and the maximum of the uncertainty measured by a general deviation measure for all the investments comprising a portfolio. We solve this bi-criteria model by first converting it into a collection of weighted sum piecewise linear convex programs, and then analysing their optimality conditions. We not only provide explicit analytical formulas for all the efficient portfolios, but also explore as a whole the set of all the efficient portfolios and its structure such as dimensionality and distribution. We generalize the classical Two-fund Theorem by providing some collections of finitely many efficient portfolios to generate or estimate the set of all the efficient portfolios. We also notice that our efficient portfolios are almost the risk parity ones in the sense that the risks are allocated equally across the investments. Moreover, we illustrate the reliability of our model by carrying out Monte Carlo simulations to test the performance of some efficient portfolios versus inefficient ones.



中文翻译:

重新审视极小极大规则下的投资组合优化

在本文中,我们重新审视了允许卖空的双准则投资组合优化模型,并在投资组合的预期收益率与所有投资组合的一般偏差度量所测得的最大不确定性之间寻求权衡。构成投资组合的投资。我们通过首先将其转换为加权和分段线性凸程序的集合来解决此双准则模型,然后分析它们的最优性条件。我们不仅为所有有效投资组合提供了明确的解析公式,而且对所有有效投资组合的集合及其维度和分布等结构进行了整体探索。我们通过提供一些有限多个有效投资组合的集合来推广经典的双基金定理,以生成或估计所有有效投资组合的集合。我们还注意到,我们的有效投资组合几乎是风险平价投资组合,因为风险在投资中被平均分配。此外,我们通过进行蒙特卡罗模拟来说明我们模型的可靠性,以测试一些有效投资组合与低效投资组合的性能。

更新日期:2021-05-29
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