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Non-Concave Utility Maximization with Transaction Costs

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  • Shuaijie Qian
  • Chen Yang

Abstract

This paper studies a finite-horizon portfolio selection problem with non-concave terminal utility and proportional transaction costs. The commonly used concavification principle for terminal value is no longer valid here, and we establish a proper theoretical characterization of this problem. We first give the asymptotic terminal behavior of the value function, which implies any transaction close to maturity only provides a marginal contribution to the utility. After that, the theoretical foundation is established in terms of a novel definition of the viscosity solution incorporating our asymptotic terminal condition. Via numerical analyses, we find that the introduction of transaction costs into non-concave utility maximization problems can prevent the portfolio from unbounded leverage and make a large short position in stock optimal despite a positive risk premium and symmetric transaction costs.

Suggested Citation

  • Shuaijie Qian & Chen Yang, 2023. "Non-Concave Utility Maximization with Transaction Costs," Papers 2307.02178, arXiv.org.
    • Handle: RePEc:arx:papers:2307.02178
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    References listed on IDEAS

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