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Optimal Investment with Stopping in Finite Horizon

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  • Xiongfei Jian
  • Xun Li
  • Fahuai Yi

Abstract

In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed dynamic optimal control and stopping problems in the existing literature, to study a manager's decision. We formulate our model to a free boundary problem of a fully nonlinear equation. Furthermore, by means of a dual transformation for the above problem, we convert the above problem to a new free boundary problem of a linear equation. Finally, we apply the theoretical results to challenging, yet practically relevant and important, risk-sensitive problems in wealth management to obtain the properties of the optimal strategy and the right time to achieve a certain level over a finite time investment horizon.

Suggested Citation

  • Xiongfei Jian & Xun Li & Fahuai Yi, 2014. "Optimal Investment with Stopping in Finite Horizon," Papers 1406.6940, arXiv.org.
    • Handle: RePEc:arx:papers:1406.6940
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    References listed on IDEAS

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    4. Jingtang Ma & Jie Xing & Harry Zheng, 2018. "Global Closed-form Approximation of Free Boundary for Optimal Investment Stopping Problems," Papers 1810.09397, arXiv.org.
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    7. Ling Wang & Kexin Chen & Mei Choi Chiu & Hoi Ying Wong, 2021. "Optimal Expansion of Business Opportunity," Papers 2112.06706, arXiv.org.

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