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A free boundary problem arising from a multi-state regime-switching stock trading model

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  • Chonghu Guan
  • Jing Peng
  • Zuo Quan Xu

Abstract

In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock that is driven by a uncertain market status process. The free boundary problem is a variational inequality system of three functions with a degenerate operator. The main contribution of this paper is that we not only prove all the four switching free boundaries are no-overlapping, monotonic and $C^{\infty}$-smooth, but also completely determine their relative localities and provide the optimal trading strategies for the stock trading problem.

Suggested Citation

  • Chonghu Guan & Jing Peng & Zuo Quan Xu, 2020. "A free boundary problem arising from a multi-state regime-switching stock trading model," Papers 2008.07082, arXiv.org.
    • Handle: RePEc:arx:papers:2008.07082
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    File URL: http://arxiv.org/pdf/2008.07082
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