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Relative risk (RR) is a statistical measure commonly used in epidemiology to compare the likelihood of a particular event occurring between two groups. This metric is important for evaluating the relationship between exposure to a specific risk factor and the probability of a particular outcome. It plays a crucial role in medical research, public health studies, and risk assessment. Relative risk quantifies how much more (or less) likely an event is to occur in an exposed group compared to an...
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Sparse and risk diversification portfolio selection.

Qian Li1, Wei Zhang2

  • 1School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620 China.

Optimization Letters
|August 8, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces the Joint Mean-Variance (JMV) model for optimal portfolio selection, integrating risk diversification and sparse asset selection. The JMV model effectively balances risk management with reduced transaction costs for better investment strategies.

Keywords:
Accelerated proximal algorithmLinear convergenceNon-convex regularizationSparse portfolio selection

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Area of Science:

  • Quantitative Finance
  • Computational Finance
  • Financial Risk Management

Background:

  • Modern portfolio management faces challenges from unpredictable market events like the 2008 financial crisis and COVID-19.
  • Over-diversification to manage portfolio risk can lead to high transaction costs and managerial complexities.

Purpose of the Study:

  • To develop an optimal portfolio selection model that integrates risk diversification with sparse asset selection.
  • To address the limitations of traditional portfolio optimization methods by incorporating sparsity and effective risk management.

Main Methods:

  • A novel Joint Mean-Variance (JMV) portfolio optimization model is proposed.
  • The model utilizes weighted piecewise quadratic approximation for sparse asset selection.
  • Marginal risk variance is incorporated as a penalty term for risk diversification.

Main Results:

  • Theoretical analysis proves that the KKT point of the JMV model is a local minimizer under specific conditions.
  • The Accelerated Proximal Gradient (APG) algorithm is introduced for efficient model solving, demonstrating linear convergence.
  • Empirical analyses validate the theoretical findings and showcase the JMV model's superior performance.

Conclusions:

  • The JMV model offers an effective framework for balancing portfolio risk diversification and sparse asset selection.
  • The APG algorithm provides an efficient computational method for solving the JMV model.
  • The proposed approach demonstrates practical advantages in portfolio risk management and asset selection.