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Optimal Investment with Herd Behaviour Using Rational Decision Decomposition

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  • Huisheng Wang
  • H. Vicky Zhao

Abstract

In this paper, we study the optimal investment problem considering the herd behaviour between two agents, including one leading expert and one following agent whose decisions are influenced by those of the leading expert. In the objective functional of the optimal investment problem, we introduce the average deviation term to measure the distance between the two agents' decisions and use the variational method to find its analytical solution. To theoretically analyze the impact of the following agent's herd behaviour on his/her decision, we decompose his/her optimal decision into a convex linear combination of the two agents' rational decisions, which we call the rational decision decomposition. Furthermore, we define the weight function in the rational decision decomposition as the following agent's investment opinion to measure the preference of his/her own rational decision over that of the leading expert. We use the investment opinion to quantitatively analyze the impact of the herd behaviour, the following agent's initial wealth, the excess return, and the volatility of the risky asset on the optimal decision. We validate our analyses through numerical experiments on real stock data. This study is crucial to understanding investors' herd behaviour in decision-making and designing effective mechanisms to guide their decisions.

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  • Huisheng Wang & H. Vicky Zhao, 2024. "Optimal Investment with Herd Behaviour Using Rational Decision Decomposition," Papers 2401.07183, arXiv.org, revised Jul 2024.
    • Handle: RePEc:arx:papers:2401.07183
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    4. David Hirshleifer & Siew Hong Teoh, 2003. "Herd Behaviour and Cascading in Capital Markets: a Review and Synthesis," European Financial Management, European Financial Management Association, vol. 9(1), pages 25-66, March.
    5. Jeffrey R. Brown & Zoran Ivković & Paul A. Smith & Scott Weisbenner, 2008. "Neighbors Matter: Causal Community Effects and Stock Market Participation," Journal of Finance, American Finance Association, vol. 63(3), pages 1509-1531, June.
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