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Optimal R &D Investment Problem with Regime-Switching

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Abstract

In this paper, we study the optimal research and development (R &D) investment problem under the framework of real options in a regime-switching environment. We assume that the firm has an R &D project whose input process with technical uncertainty is affected by different regimes. By the method of dynamic programming, we have obtained the related Hamilton–Jacobi–Bellman (HJB) equation and solved it in three different cases. Then, the optimal solution for our model is constructed and the related verification theorem is also provided. Finally, some numerical examples are given to investigate the properties of our model.

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Notes

  1. If \(n=1\) represents the ’unfrindly’ regime and \(n=2\) represents the ’friendly’ regime, the result is similar. Thus, we omit the discussion here, similarly hereinafter.

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Acknowledgements

The authors would like to express deep gratitude to the reviewers and the editor for their very helpful suggestions and comments, which have helped us to substantially improve the presentation and quality of this manuscript.

Funding

This work was supported in part by the Fundamental Research Funds for the Central Universities (JBK2101005), in part by the National Natural Science of Foundation of China (11801462, 12171339).

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Authors and Affiliations

  1. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, People’s Republic of China

    Ming-hui Wang & Jia Yue

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, Sichuan, People’s Republic of China

    Nan-jing Huang

Authors
  1. Ming-hui Wang
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  2. Jia Yue
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Correspondence to Nan-jing Huang.

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Communicated by Kok Lay Teo.

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Wang, Mh., Yue, J. & Huang, Nj. Optimal R &D Investment Problem with Regime-Switching. J Optim Theory Appl 202, 878–896 (2024). https://doi.org/10.1007/s10957-024-02451-0

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