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Valuation of R&D projects of new energy vehicles based on generalized mixed sub-fractional Brownian motion under fuzzy environment

Author

Listed:
  • Zhang, Weiting
  • He, Guitian
  • Luo, Maokang
  • Liang, Wenjie

Abstract

The industry and investors are closely monitoring the valuation of research and development (R&D) projects related to new energy vehicles (NEVs) as their technology advances rapidly. However, standard techniques of valuation often fail to describe the full value of R&D initiatives in an uncertain market environment, due to the significant technical hazards and uncertain results associated with these projects. To address this issue, this study creatively introduces a generalized mixed sub-fractional Brownian motion (GMSFBM) based valuation method for compound real options in the NEV R&D projects. In order to more accurately characterize the technical and financial risks at every stage of the R&D process, this paper combines stochastic processes with compound real option theory. Significantly, to derive the assessment model for NEV R&D projects, a fuzzy partial differential equation (FPDE) of the five-fold compound real option model is constructed using Itô's lemma. Moreover, asymmetric trapezoidal fuzzy parameters are also introduced by the valuation model to characterize the uncertainty of the NEV R&D projects. Finally, numerical experiments are conducted to validate the effectiveness and practicality of the GMSFBM model in the appraisement of the NEV R&D projects, providing new quantitative analysis tools and methods for project decision-making.

Suggested Citation

  • Zhang, Weiting & He, Guitian & Luo, Maokang & Liang, Wenjie, 2025. "Valuation of R&D projects of new energy vehicles based on generalized mixed sub-fractional Brownian motion under fuzzy environment," Applied Mathematics and Computation, Elsevier, vol. 507(C).
    • Handle: RePEc:eee:apmaco:v:507:y:2025:i:c:s0096300325002851
    DOI: 10.1016/j.amc.2025.129559
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    1. Mombello, Bruno & Olsina, Fernando & Pringles, Rolando, 2023. "Valuing photovoltaic power plants by compound real options," Renewable Energy, Elsevier, vol. 216(C).
    2. Rodolphe Durand & Robert M. Grant & Tammy L. Madsen & Lenos Trigeorgis & Jeffrey J. Reuer, 2017. "Real options theory in strategic management," Strategic Management Journal, Wiley Blackwell, vol. 38(1), pages 42-63, January.
    3. Loncar, Dragan & Milovanovic, Ivan & Rakic, Biljana & Radjenovic, Tamara, 2017. "Compound real options valuation of renewable energy projects: The case of a wind farm in Serbia," Renewable and Sustainable Energy Reviews, Elsevier, vol. 75(C), pages 354-367.
    4. Sun, Ya-Fang & Zhang, Yue-Jun & Su, Bin, 2022. "Impact of government subsidy on the optimal R&D and advertising investment in the cooperative supply chain of new energy vehicles," Energy Policy, Elsevier, vol. 164(C).
    5. Han, Jing & Guo, Ju-E & Cai, Xun & Lv, Cheng & Lev, Benjamin, 2022. "An analysis on strategy evolution of research & development in cooperative innovation network of new energy vehicle within policy transition period," Omega, Elsevier, vol. 112(C).
    6. Ma, Yiju & Chapman, Archie C. & Verbič, Gregor, 2022. "Valuation of compound real options for co-investment in residential battery systems," Applied Energy, Elsevier, vol. 318(C).
    7. Cassimon, D. & De Backer, M. & Engelen, P.J. & Van Wouwe, M. & Yordanov, V., 2011. "Incorporating technical risk in compound real option models to value a pharmaceutical R&D licensing opportunity," Research Policy, Elsevier, vol. 40(9), pages 1200-1216.
    8. Cassimon, D. & Engelen, P. J. & Thomassen, L. & Van Wouwe, M., 2004. "The valuation of a NDA using a 6-fold compound option," Research Policy, Elsevier, vol. 33(1), pages 41-51, January.
    9. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    10. Shapiro, Arnold F., 2009. "Fuzzy random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 307-314, April.
    11. Danny Cassimon & Peter‐Jan Engelen & Linda Peters & Martin Prowse, 2023. "Valuing investments in the Global Carbon Market Mechanism as compound real options: Lessons from the Clean Development Mechanism," Sustainable Development, John Wiley & Sons, Ltd., vol. 31(5), pages 3443-3458, October.
    12. Xiandong Wang & Jianmin He & Shouwei Li, 2014. "Compound Option Pricing under Fuzzy Environment," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, March.
    13. Wang, Wei & Cai, Guanghui & Tao, Xiangxing, 2021. "Pricing geometric asian power options in the sub-fractional brownian motion environment," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    14. Xiandong Wang & Jianmin He & Shouwei Li, 2014. "Compound Option Pricing under Fuzzy Environment," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    15. Won-Joon Jang & Jeong-Dong Lee, 2011. "The Application Of Real Options Theory In Defense R&D Projects: An Eight-Fold Sequential Compound Option Model," International Journal of Innovation and Technology Management (IJITM), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 95-112.
    16. Panhong Cheng & Zhihong Xu & Zexing Dai, 2023. "Valuation of vulnerable options with stochastic corporate liabilities in a mixed fractional Brownian motion environment," Mathematics and Financial Economics, Springer, volume 17, number 3, June.
    17. Ma, Pengcheng & Taghipour, Mehran & Cattani, Carlo, 2024. "Option pricing in the illiquid markets under the mixed fractional Brownian motion model," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    18. Ma, Pengcheng & Najafi, Alireza & Gomez-Aguilar, J.F., 2024. "Sub mixed fractional Brownian motion and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    19. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    20. Axel A. Araneda & Nils Bertschinger, 2020. "The sub-fractional CEV model," Papers 2001.06412, arXiv.org, revised Mar 2021.
    21. Wang, Song, 2024. "Pricing European call options with interval-valued volatility and interest rate," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    22. Araneda, Axel A. & Bertschinger, Nils, 2021. "The sub-fractional CEV model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    23. Tolga, A. Cagri, 2020. "Real options valuation of an IoT based healthcare device with interval Type-2 fuzzy numbers," Socio-Economic Planning Sciences, Elsevier, vol. 69(C).
    24. Grillo, Sebastian & Blanco, Gerardo & Schaerer, Christian E., 2015. "Path integration for real options," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 120-132.
    25. Ahmadian, D. & Ballestra, L.V. & Shokrollahi, F., 2022. "A Monte-Carlo approach for pricing arithmetic Asian rainbow options under the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    26. Zhao, Pingping & Wang, Tong & Song, Aimin & Chen, Peimin, 2023. "Valuing new drug R&D project under economic fluctuation, technical risks and subjective uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
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