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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.

References

  1. Bensoussan, A., Hoe, S.R., Yan, Z.F., Yin, G.: Real options with competition and regime switching. Math. Financ. 27, 224–250 (2017)

    Article  MathSciNet  Google Scholar 

  2. Bensoussan, A., Yan, Z.F., Yin, G.: Threshold-type policies for real options using regime-switching models. SIAM J. Financ. Math. 3, 667–689 (2012)

    Article  MathSciNet  Google Scholar 

  3. Bizan, O.: The determinants of success of R &D projects: evidence from American-Israeli research alliances. Res. Policy 32, 1619–1640 (2003)

    Article  Google Scholar 

  4. Choi, J.P.: Cooperative R &D with product market competition. Int. J. Ind. Organ. 11, 553–571 (1993)

    Article  Google Scholar 

  5. Chronopoulos, M., Lumbreras, S.: Optimal regime switching under risk aversion and uncertainty. Eur. J. Oper. Res. 256, 543–555 (2017)

    Article  MathSciNet  Google Scholar 

  6. Cohen, W., Levin, R., Mowery, D.: Firm size and R &D intensity: a re-examination. J. Ind. Econ. 35, 543–565 (1987)

    Article  Google Scholar 

  7. Cooper, R.G.: An empirically derived new product project selection model. IEEE Trans. Eng. Manag. 28, 54–61 (1981)

    Article  Google Scholar 

  8. Dai, M., Zhang, Q., Zhu, J.: Trend following trading under a regime switching model. SIAM J. Financ. Math. 1, 780–810 (2010)

    Article  MathSciNet  Google Scholar 

  9. Dasgupta, P., Stiglitz, J.: Industrial structure and the nature of innovative activity. Econ. J. 90, 266–293 (1980)

    Article  Google Scholar 

  10. Elliott, R.J., Siu, T.K.: On risk minimizing portfolios under a Markovian regime-switching Black–Scholes economy. Ann. Oper. Res. 176, 271–291 (2010)

    Article  MathSciNet  Google Scholar 

  11. Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems. Springer, New York (1993)

    Google Scholar 

  12. Huchzermeier, A., Loch, C.H.: Project management under risk: using the real options approach to evaluate flexibility in R &D. Manage. Sci. 47, 85–101 (2001)

    Article  Google Scholar 

  13. Kort, P.M.: Optimal R &D investment of the firm. OR Spektrum 20, 155–164 (1998)

    Article  MathSciNet  Google Scholar 

  14. Koussis, N., Martzoukos, S.H., Trigeorgis, L.: Real R &D options with time-to-learn and learning-by-doing. Ann. Oper. Res. 151, 29–55 (2007)

    Article  MathSciNet  Google Scholar 

  15. Lin, D.: Accelerability vs. scalability: R &D investment under financial constraints and competition. Manag. Sci. 69, 4078–4107 (2023)

    Article  Google Scholar 

  16. Moawia, A.: A note on the theory of the firm under multiple uncertainties. Eur. J. Oper. Res. 251, 341–343 (2016)

    Article  MathSciNet  Google Scholar 

  17. Nishihara, M.: Valuation of R &D investment under technological, market, and rival preemption uncertainty. Manag. Decis. Econ. 39, 200–212 (2018)

    Article  Google Scholar 

  18. Nishihara, M.: Closed-form solution to a real option problem with regime switching. Oper. Res. Lett. 48, 703–707 (2020)

    Article  MathSciNet  Google Scholar 

  19. Osmolovskii, N.P., Maurer, H.: Applications to Regular and Bang-Bang Control. Society for Industrial and Applied Mathematics, Philadelphia, PA (2012)

    Book  Google Scholar 

  20. Pennings, E., Sereno, L.: Evaluating pharmaceutical R &D under technical and economic uncertainty. Eur. J. Oper. Res. 212, 374–385 (2011)

    Article  Google Scholar 

  21. Pindyck, R.S.: Investments of uncertain cost. J. Financ. Econ. 34, 53–76 (1993)

    Article  Google Scholar 

  22. Sendstad, L.H., Chronopoulos, M.: Strategic technology switching under risk aversion and uncertainty. J. Econ. Dyn. Control 126, 103918 (2021)

    Article  MathSciNet  Google Scholar 

  23. Sotomayor, L., Cadenillas, A.: Explicit solutions of consumption investment problems in financial markets with regime switching. Math. Financ. 19, 251–279 (2009)

    Article  MathSciNet  Google Scholar 

  24. Teschl, G.: Ordinary Differential Equations and Dynamical Systems. American Mathematical Society, Providence (2012)

    Book  Google Scholar 

  25. Villani, G., Biancardi, M.: An evolutionary game approach in international environmental agreements with R &D investments. Comput. Econ. 54, 1027–1042 (2019)

    Article  Google Scholar 

  26. Wang, M.H., Huang, N.J., O’Regan, D.: Optimal product release time for a new high-tech startup firm under technical uncertainty. J. Ind. Manag. Optim. 19, 321–337 (2023)

    Article  MathSciNet  Google Scholar 

  27. Wang, M.H., Huang, N.J.: Robust optimal R &D investment under technical uncertainty in a regime-switching environment. Optimization 71, 1557–1578 (2022)

    Article  MathSciNet  Google Scholar 

  28. Whalley, A.E.: Optimal R &D investment for a risk-averse entrepreneur. J. Econ. Dyn. Control 35, 413–429 (2011)

    Article  MathSciNet  Google Scholar 

  29. Yu, X.N., Lan, Y.F., Zhao, R.Q.: Cooperation royalty contract design in research and development alliances: Help vs. knowledge-sharing. Eur. J. Oper. Res. 268, 740–754 (2018)

    Article  MathSciNet  Google Scholar 

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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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  3. Nan-jing Huang
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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 (2024). https://doi.org/10.1007/s10957-024-02451-0

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