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A kind of optimal investment problem under inflation and uncertain time horizon

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  • Huang, Zongyuan
  • Wang, Haiyang
  • Wu, Zhen

Abstract

In this paper, we study a kind of optimal investment problem under inflation and uncertain time horizon. It can be generally formulated into a stochastic optimal control problem. In particular for the constant relative risk aversion utility, we employ the method of completion of squares to give an explicit form of optimal portfolio and maximum utility by the solution of a stochastic Riccati equation, whose wellposedness is obtained and also of significance in its own right. The most distinguishing result of our work is that the randomness of exit time actually affects not only the optimal portfolio but also the maximum utility in the case of stochastic market parameters. Moreover, we present several numerical examples to show the application of theoretical results and further discuss the influence of inflation and random time horizon from the economic viewpoint.

Suggested Citation

  • Huang, Zongyuan & Wang, Haiyang & Wu, Zhen, 2020. "A kind of optimal investment problem under inflation and uncertain time horizon," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    • Handle: RePEc:eee:apmaco:v:375:y:2020:i:c:s0096300320300539
    DOI: 10.1016/j.amc.2020.125084
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    Cited by:

    1. Tian Chen & Ruyi Liu & Zhen Wu, 2022. "Continuous-time mean-variance portfolio selection under non-Markovian regime-switching model with random horizon," Papers 2205.06434, arXiv.org.
    2. Yumo Zhang, 2023. "Utility maximization in a stochastic affine interest rate and CIR risk premium framework: a BSDE approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 97-128, June.
    3. Mondher Bellalah & Akeb Hakim & Kehan Si & Detao Zhang, 2022. "Long term optimal investment with regime switching: inflation, information and short sales," Annals of Operations Research, Springer, vol. 313(2), pages 1373-1386, June.

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