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Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal Wealth

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  • Xue Dong He

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong)

  • Zhaoli Jiang

    (Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong)

Abstract

In a market that consists of multiple stocks and one risk-free asset whose mean return rates and volatility are deterministic, we study a continuous-time mean-variance portfolio selection problem in which an agent is subject to a constraint that the expectation of the agent’s terminal wealth must exceed a target and minimize the variance of the agent’s terminal wealth. The agent can revise the expected terminal wealth target dynamically to adapt to the change of the agent’s current wealth, and we consider the following three targets: (i) the agent’s current wealth multiplied by a target expected gross return rate, (ii) the risk-free payoff of the agent’s current wealth plus a premium, and (iii) a weighted average of the risk-free payoff of the agent’s current wealth and a preset aspiration level. We derive the so-called equilibrium strategy in closed form for each of the three targets and find that the agent effectively minimizes the variance of the instantaneous change of the agent’s wealth subject to a certain constraint on the expectation of the instantaneous change of the agent’s wealth.

Suggested Citation

  • Xue Dong He & Zhaoli Jiang, 2022. "Mean-Variance Portfolio Selection with Dynamic Targets for Expected Terminal Wealth," Mathematics of Operations Research, INFORMS, vol. 47(1), pages 587-615, February.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:1:p:587-615
    DOI: 10.1287/moor.2021.1142
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    References listed on IDEAS

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    2. De Gennaro Aquino, Luca & Sornette, Didier & Strub, Moris S., 2023. "Portfolio selection with exploration of new investment assets," European Journal of Operational Research, Elsevier, vol. 310(2), pages 773-792.

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