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Asymptotic analysis for target asset portfolio allocation with small transaction costs

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  • Liu, Cong
  • Zheng, Harry

Abstract

In this paper we discuss the asset allocation in the presence of small proportional transaction costs. The objective is to keep the asset portfolio close to a target portfolio and at the same time to reduce the trading cost in doing so. We derive the variational inequality and prove a verification theorem. Furthermore, we apply the second order asymptotic expansion method to characterize explicitly the optimal no transaction region when the transaction cost is small and show that the boundary points are asymmetric in relation to the target portfolio position, in contrast to the symmetric relation when only the first order asymptotic expansion method is used, and the leading order is a constant proportion of the cubic root of the small transaction cost. In addition, we use the asymptotic results for the boundary points and obtain an expansion for the value function. The results are illustrated in the numerical example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:insuma:v:66:y:2016:i:c:p:59-68
    DOI: 10.1016/j.insmatheco.2015.10.014
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    Cited by:

    1. Yue, Wei & Wang, Yuping, 2017. "A new fuzzy multi-objective higher order moment portfolio selection model for diversified portfolios," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 124-140.
    2. Kenneth Bruhn & Ninna Reitzel Jensen & Mogens Steffensen, 2016. "Smooth investment," Annals of Finance, Springer, vol. 12(3), pages 335-361, December.

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    More about this item

    Keywords

    Target asset portfolio allocation; Tracking error; Proportional transaction costs; Magnus expansion; Asymptotic analysis;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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