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Smooth investment

Author

Listed:
  • Kenneth Bruhn

    (University of Copenhagen)

  • Ninna Reitzel Jensen

    (University of Copenhagen)

  • Mogens Steffensen

    (University of Copenhagen)

Abstract

In the classical portfolio optimization problem considered by Merton, the resulting constant proportion investment plan requires a diffusive trading strategy. This means that, within any arbitrarily small time interval, the investor must impractically both buy and sell stocks. We study the problems of a mean-square and a power utility investor for whom the trading strategy is constrained to be smooth, i.e. nondiffusive. This means that over sufficiently small time intervals, the investor is either a seller or a buyer of stocks. The mathematical framework is built around quadratic objectives such that trading activity is punished quadratically. Mean-square utility is quadratic, and power utility is covered by quadratic punishment of distance to Merton’s power utility portfolio. We present semi-explicit solutions and, in a series of numerical illustrations, show the impact of trading constraints on the portfolio decision over the investment horizon.

Suggested Citation

  • Kenneth Bruhn & Ninna Reitzel Jensen & Mogens Steffensen, 2016. "Smooth investment," Annals of Finance, Springer, vol. 12(3), pages 335-361, December.
    • Handle: RePEc:kap:annfin:v:12:y:2016:i:3:d:10.1007_s10436-016-0283-7
    DOI: 10.1007/s10436-016-0283-7
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    References listed on IDEAS

    as
    1. Bruhn, Kenneth & Steffensen, Mogens, 2013. "Optimal smooth consumption and annuity design," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2693-2701.
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    5. Chellathurai, Thamayanthi & Draviam, Thangaraj, 2007. "Dynamic portfolio selection with fixed and/or proportional transaction costs using non-singular stochastic optimal control theory," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2168-2195, July.
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    7. Liu, Cong & Zheng, Harry, 2016. "Asymptotic analysis for target asset portfolio allocation with small transaction costs," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 59-68.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Smooth investment; Diffusive trading; Trading costs; Power utility; Mean-square utility;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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