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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.
    2. Longstaff, Francis A, 2001. "Optimal Portfolio Choice and the Valuation of Illiquid Securities," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 407-431.
    3. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
    4. M. H. A. Davis & A. R. Norman, 1990. "Portfolio Selection with Transaction Costs," Mathematics of Operations Research, INFORMS, vol. 15(4), pages 676-713, November.
    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.
    6. Peter Bank & Dietmar Baum, 2004. "Hedging and Portfolio Optimization in Financial Markets with a Large Trader," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 1-18, January.
    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.
    8. Stanley Pliska & Kiyoshi Suzuki, 2004. "Optimal tracking for asset allocation with fixed and proportional transaction costs," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 233-243.
    9. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    10. Halil Mete Soner & Mirjana Vukelja, 2013. "Utility Maximization in an Illiquid Market," Swiss Finance Institute Research Paper Series 13-17, Swiss Finance Institute.
    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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