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Reaching goals under ambiguity: Continuous-time optimal portfolio selection

Author

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  • Ji, Shaolin
  • Shi, Xiaomin

Abstract

In this paper, the problem of reaching goals for an investor in the financial market is studied. We follow the context of Jin and Zhou (2015) who studied the continuous-time optimal portfolio selection in which the appreciation rates are only known to be in a certain convex closed set. The cost functional in our problem is of type I{x≥1} which is not concave or convex, even not continuous, we prove that the min–max theorem is still applicable. Via PDE approach, we construct the optimal portfolio strategy. At last, we obtain the saddle point for our problem explicitly.

Suggested Citation

  • Ji, Shaolin & Shi, Xiaomin, 2018. "Reaching goals under ambiguity: Continuous-time optimal portfolio selection," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 63-69.
    • Handle: RePEc:eee:stapro:v:137:y:2018:i:c:p:63-69
    DOI: 10.1016/j.spl.2018.01.010
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    References listed on IDEAS

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    1. Chen, Zengjing & Kulperger, Reg & Wei, Gang, 2005. "A comonotonic theorem for BSDEs," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 41-54, January.
    2. Ji, Shaolin & Peng, Shige, 2008. "Terminal perturbation method for the backward approach to continuous time mean-variance portfolio selection," Stochastic Processes and their Applications, Elsevier, vol. 118(6), pages 952-967, June.
    3. Tim Leung & Qingshuo Song & Jie Yang, 2013. "Outperformance portfolio optimization via the equivalence of pure and randomized hypothesis testing," Finance and Stochastics, Springer, vol. 17(4), pages 839-870, October.
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    Cited by:

    1. Gloria Gonzalez‐Rivera & Yun Luo & Esther Ruiz, 2020. "Prediction regions for interval‐valued time series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 373-390, June.
    2. Xiaonan Chen & Jianfeng Song, 2022. "Influence Path Analysis of Rural Household Portfolio Selection: A Empirical Study Using Structural Equation Modelling Method," The Journal of Real Estate Finance and Economics, Springer, vol. 64(2), pages 298-322, February.

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