The worst-case scenario: robust portfolio optimization with discrete distributions and transaction costs

Ebenezer Fiifi Emire Atta Mills; Ebenezer Fiifi Emire Atta Mills

doi:10.3934/math.20241018

AIMS Mathematics

2024, Volume 9, Issue 8: 20919-20938. doi: 10.3934/math.20241018

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Research article

The worst-case scenario: robust portfolio optimization with discrete distributions and transaction costs

Ebenezer Fiifi Emire Atta Mills ^{1,2
,
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1.
School of Mathematical Sciences, Wenzhou-Kean University, Wenzhou, China
2.
Academy of Research for Sustainability (AIRs), Wenzhou-Kean University, Wenzhou, China

Received: 14 March 2024 Revised: 27 May 2024 Accepted: 30 May 2024 Published: 28 June 2024
MSC : 91B05, 91G10

This research introduces min-max portfolio optimization models that incorporating transaction costs and focus on robust Entropic value-at-risk. This study offers a unified approach to handl the distribution of random parameters that affect the reward and risk aspects. Utilizing the duality theorem, the study transforms the optimization models into manageable forms, thereby accommodating the underlying random variables' discrete box and ellipsoidal distributions. The impact of transaction costs on optimal portfolio selection is examined through numerical examples under a robust return-risk framework. The results underscore the importance of the proposed model in safeguarding capital and reducing exposure to extreme risks, thus outperforming other strategies documented in the literature. This demonstrates the model's effectiveness in balancing maximizing returns and minimizing potential losses, making it a valuable tool for investors that seek to navigate uncertain financial markets.
- portfolio optimization,
- entropic value-at-risk,
- transaction costs,
- uncertainty,
- robust return-risk
Citation: Ebenezer Fiifi Emire Atta Mills. The worst-case scenario: robust portfolio optimization with discrete distributions and transaction costs[J]. AIMS Mathematics, 2024, 9(8): 20919-20938. doi: 10.3934/math.20241018

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Abstract

This research introduces min-max portfolio optimization models that incorporating transaction costs and focus on robust Entropic value-at-risk. This study offers a unified approach to handl the distribution of random parameters that affect the reward and risk aspects. Utilizing the duality theorem, the study transforms the optimization models into manageable forms, thereby accommodating the underlying random variables' discrete box and ellipsoidal distributions. The impact of transaction costs on optimal portfolio selection is examined through numerical examples under a robust return-risk framework. The results underscore the importance of the proposed model in safeguarding capital and reducing exposure to extreme risks, thus outperforming other strategies documented in the literature. This demonstrates the model's effectiveness in balancing maximizing returns and minimizing potential losses, making it a valuable tool for investors that seek to navigate uncertain financial markets.

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