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Dynamic mean–variance problem with frictions

Author

Listed:
  • Alain Bensoussan

    (University of Texas at Dallas
    City University of Hong Kong)

  • Guiyuan Ma

    (Xi’an Jiaotong University)

  • Chi Chung Siu

    (The Hang Seng University of Hong Kong)

  • Sheung Chi Phillip Yam

    (The Chinese University of Hong Kong)

Abstract

We study a dynamic mean–variance portfolio selection problem with return predictability and trading frictions from price impact. Applying mean-field type control theory, we provide a characterisation of an equilibrium trading strategy for an investor facing stochastic investment opportunities. An explicit equilibrium strategy is derived in terms of the solution to a generalised matrix Riccati differential equation, and a sufficient condition is also provided to ensure the latter’s well-posedness. Our solution indicates that the investor should trade gradually towards a target portfolio which accounts for return predictability, price impact and time-consistency. Moreover, an asymptotic analysis around small liquidity costs shows that the investor’s target portfolio is an equilibrium portfolio without price impact in the first-order sense, and that her first-order approximated value function does not deteriorate significantly for sufficiently small liquidity costs. Finally, our numerical results demonstrate that the target portfolio is more conservative than an equilibrium portfolio without price impact.

Suggested Citation

  • Alain Bensoussan & Guiyuan Ma & Chi Chung Siu & Sheung Chi Phillip Yam, 2022. "Dynamic mean–variance problem with frictions," Finance and Stochastics, Springer, vol. 26(2), pages 267-300, April.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:2:d:10.1007_s00780-022-00474-x
    DOI: 10.1007/s00780-022-00474-x
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    References listed on IDEAS

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    Cited by:

    1. Ma, Guiyuan & Siu, Chi Chung & Zhu, Song-Ping, 2022. "Portfolio choice with return predictability and small trading frictions," Economic Modelling, Elsevier, vol. 111(C).

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    More about this item

    Keywords

    Dynamic mean–variance problem; Price impact; Time-inconsistency; Asymptotics; Mean-field type control problems;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

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