<p>Regret and disappointment, as the negative sentiments of investment, have been widely studied in the field of behavioral finance. However, classical variances rarely reflect the investors’ psychology when measuring risk. To comprehensively consider the influence of regret and disappointment in portfolio, we extend classical variances to regret variances and disappointment variances based on regret and disappointment theories. Under the above variance frameworks, a new regret-disappointment portfolio model is constructed. Combining the advantages of standard semi-deviation and relative-deviation, we define a novel global-regret-standard-deviation. In addition, we use the standard deviation and subjective value as <i>x</i> and <i>y</i> coordinates to construct a new evaluation system. Considering the rare simulation of investors’ behavior in particle swarm optimization (PSO) algorithm previously, we also propose an improved regret particle swarm optimization (R-PSO) algorithm in three aspects: by adopting the probability weight function of prospect theory to centralize the random numbers; by using inertia factor with the “regret” parameter to describe investors’ sentiment; by adding cross-mutation operations to PSO to enhance search capability and maintain population diversity. Finally, in the experiments study, regret-disappointment model is given to verify the feasibility by parameter sensitivity analysis, whose results indicate that regret-disappointment preferences can lead to different investment choices. Further, our improved R-PSO algorithm is demonstrated more stably and effectively in global optima by risk comparison and convergence analysis.</p>

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Portfolio with Improved Particle Swarm Optimization Based on Regret Theory and Disappointment Theory

  • Xue Deng,
  • Mengchan Liu,
  • Keyao Zheng,
  • Zhenghua Du,
  • Wen Zhou,
  • Xinyi Jiang

摘要

Regret and disappointment, as the negative sentiments of investment, have been widely studied in the field of behavioral finance. However, classical variances rarely reflect the investors’ psychology when measuring risk. To comprehensively consider the influence of regret and disappointment in portfolio, we extend classical variances to regret variances and disappointment variances based on regret and disappointment theories. Under the above variance frameworks, a new regret-disappointment portfolio model is constructed. Combining the advantages of standard semi-deviation and relative-deviation, we define a novel global-regret-standard-deviation. In addition, we use the standard deviation and subjective value as x and y coordinates to construct a new evaluation system. Considering the rare simulation of investors’ behavior in particle swarm optimization (PSO) algorithm previously, we also propose an improved regret particle swarm optimization (R-PSO) algorithm in three aspects: by adopting the probability weight function of prospect theory to centralize the random numbers; by using inertia factor with the “regret” parameter to describe investors’ sentiment; by adding cross-mutation operations to PSO to enhance search capability and maintain population diversity. Finally, in the experiments study, regret-disappointment model is given to verify the feasibility by parameter sensitivity analysis, whose results indicate that regret-disappointment preferences can lead to different investment choices. Further, our improved R-PSO algorithm is demonstrated more stably and effectively in global optima by risk comparison and convergence analysis.