IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i8p1142-d1373373.html
   My bibliography  Save this article

Novel Numerical Investigation of Reaction Diffusion Equation Arising in Oil Price Modeling

Author

Listed:
  • Fehaid Salem Alshammari

    (Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia)

Abstract

Consideration is given to a reaction–diffusion free boundary value problem with one or two turning points arising in oil price modeling. First, an exact (analytical) solution to the reduced problem (i.e., no diffusion term) was obtained for some given parameters. The space–time Chebyshev pseudospectral and superconsistent Chebyshev collocation method is proposed for both reaction diffusion (RDFBP) and reduced free boundary value problem. Error bounds on the discrete L 2 –norm and Sobolev norm ( H p ) are presented. Adaptively graded intervals were introduced and used according to the value of turning points to avoid the twin boundary layers phenomena. Excellent convergent (spectrally) and stable results for some special turning points were obtained for both reduced and RDFBP equations on an adaptively graded interval and this has been documented for the first time.

Suggested Citation

  • Fehaid Salem Alshammari, 2024. "Novel Numerical Investigation of Reaction Diffusion Equation Arising in Oil Price Modeling," Mathematics, MDPI, vol. 12(8), pages 1-17, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1142-:d:1373373
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/8/1142/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/8/1142/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Schwartz, Eduardo S, 1997. "The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-973, July.
    2. Mohammed A. Aba Oud & Joanna Goard, 2015. "Stochastic Models for Oil Prices and the Pricing of Futures on Oil," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(2), pages 189-206, April.
    3. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    4. Joanna Goard & Mohammed AbaOud, 2023. "A Bimodal Model for Oil Prices," Mathematics, MDPI, vol. 11(10), pages 1-26, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joanna Goard & Mohammed AbaOud, 2023. "A Bimodal Model for Oil Prices," Mathematics, MDPI, vol. 11(10), pages 1-26, May.
    2. Armstrong, Margaret & Langrené, Nicolas & Petter, Renato & Chen, Wen & Petter, Carlos, 2019. "Accounting for tailings dam failures in the valuation of mining projects," Resources Policy, Elsevier, vol. 63(C), pages 1-1.
    3. Mohammed A. Aba Oud & Joanna Goard, 2015. "Valuation Of Options On Oil Futures Under The 3/4 Oil Price Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-12, December.
    4. Bühler, Wolfgang & Korn, Olaf, 1998. "Hedging langfristiger Lieferverpflichtungen mit kurzfristigen Futures: möglich oder unmöglich?," ZEW Discussion Papers 98-20, ZEW - Leibniz Centre for European Economic Research.
    5. Nguyen, Duc Binh Benno & Prokopczuk, Marcel, 2019. "Jumps in commodity markets," Journal of Commodity Markets, Elsevier, vol. 13(C), pages 55-70.
    6. Abdullah Almansour and Margaret Insley, 2016. "The Impact of Stochastic Extraction Cost on the Value of an Exhaustible Resource: An Application to the Alberta Oil Sands," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2).
    7. Seiji Harikae & James S. Dyer & Tianyang Wang, 2021. "Valuing Real Options in the Volatile Real World," Production and Operations Management, Production and Operations Management Society, vol. 30(1), pages 171-189, January.
    8. Chen, Ruoran & Deng, Tianhu & Huang, Simin & Qin, Ruwen, 2015. "Optimal crude oil procurement under fluctuating price in an oil refinery," European Journal of Operational Research, Elsevier, vol. 245(2), pages 438-445.
    9. Björn Lutz, 2010. "Pricing of Derivatives on Mean-Reverting Assets," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-02909-7, October.
    10. Insley, Margaret, 2017. "Resource extraction with a carbon tax and regime switching prices: Exercising your options," Energy Economics, Elsevier, vol. 67(C), pages 1-16.
    11. Luis M. Abadie & José M. Chamorro, 2009. "Monte Carlo valuation of natural gas investments," Review of Financial Economics, John Wiley & Sons, vol. 18(1), pages 10-22, January.
    12. Xiao, Chang & Florescu, Ionut & Zhou, Jinsheng, 2020. "A comparison of pricing models for mineral rights: Copper mine in China," Resources Policy, Elsevier, vol. 65(C).
    13. Insley, M.C. & Wirjanto, T.S., 2010. "Contrasting two approaches in real options valuation: Contingent claims versus dynamic programming," Journal of Forest Economics, Elsevier, vol. 16(2), pages 157-176, April.
    14. Mirantes, Andrés García & Población, Javier & Serna, Gregorio, 2013. "The stochastic seasonal behavior of energy commodity convenience yields," Energy Economics, Elsevier, vol. 40(C), pages 155-166.
    15. Gonzalo Cortazar & Cristobal Millard & Hector Ortega & Eduardo S. Schwartz, 2019. "Commodity Price Forecasts, Futures Prices, and Pricing Models," Management Science, INFORMS, vol. 65(9), pages 4141-4155, September.
    16. Max F. Schöne & Stefan Spinler, 2017. "A four-factor stochastic volatility model of commodity prices," Review of Derivatives Research, Springer, vol. 20(2), pages 135-165, July.
    17. Schwartz, Eduardo, 1998. "Valuing long-term commodity assets," Journal of Energy Finance & Development, Elsevier, vol. 3(2), pages 85-99.
    18. Ozorio, Luiz de Magalhães & Bastian-Pinto, Carlos de Lamare & Baidya, Tara Keshar Nanda & Brandão, Luiz Eduardo Teixeira, 2013. "Investment decision in integrated steel plants under uncertainty," International Review of Financial Analysis, Elsevier, vol. 27(C), pages 55-64.
    19. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2015. "Pricing of Long-dated Commodity Derivatives with Stochastic Volatility and Stochastic Interest Rates," Research Paper Series 366, Quantitative Finance Research Centre, University of Technology, Sydney.
    20. Amir Yaron & Leonid Kogan & Dmitry Livdan, 2004. "Futures Prices in a Production Economy with Investment Constraints," 2004 Meeting Papers 128, Society for Economic Dynamics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1142-:d:1373373. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.