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Optimal investment with transaction costs based on exponential utility function: a parabolic double obstacle problem

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Abstract

This paper concerns optimal investment problem with proportional transaction costs and finite time horizon based on exponential utility function. Using a partial differential equation approach, we reveal that the problem is equivalent to a parabolic double obstacle problem involving two free boundaries that correspond to the optimal buying and selling policies. Numerical examples are obtained by the binomial method.

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    Qun-fang Bao, Jing-yang Yang & Sheng-hong Li

  2. Jingdezhen Ceramic Institute, Jiangxi, 333403, China

    Chao Sun

Authors
  1. Qun-fang Bao
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  2. Jing-yang Yang
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  3. Chao Sun
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  4. Sheng-hong Li
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Corresponding author

Correspondence to Qun-fang Bao.

Additional information

Supported by the Key Grant Project of Chinese Ministry of Education (NO.309018), National Natural Science Foundation of China (NO.70973104, NO.11171304) and Zhejiang Provincial Natural Science Foundation of China (NO.Y6110023).

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Bao, Qf., Yang, Jy., Sun, C. et al. Optimal investment with transaction costs based on exponential utility function: a parabolic double obstacle problem. Appl. Math. J. Chin. Univ. 26, 483–492 (2011). https://doi.org/10.1007/s11766-011-2294-5

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  • DOI: https://doi.org/10.1007/s11766-011-2294-5

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