IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i5p722-d1348574.html
   My bibliography  Save this article

Concepts of Statistical Causality and Strong and Weak Properties of Predictable Representation

Author

Listed:
  • Dragana Valjarević

    (Department of Mathematics, Faculty of Sciences and Mathematics, University of Pristina in Kosovska Mitrovica, 38220 Kosovska Mitrovica, Serbia)

Abstract

The paper considers the statistical concept of causality in continuous time, which is based on Granger’s definition of causality. We give necessary and sufficient conditions, in terms of statistical causality, for the preservation of the strong property of predictable representation for stopped martingales when filtration is decreased. This concept of causality is also connected to the preservation of the strong property of predictable representation under a change in measure. In addition, we give conditions, in terms of statistical causality, for martingales to have strong and weak properties of predictable representation. The results are applied to the problem of pricing claims in incomplete financial markets.

Suggested Citation

  • Dragana Valjarević, 2024. "Concepts of Statistical Causality and Strong and Weak Properties of Predictable Representation," Mathematics, MDPI, vol. 12(5), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:722-:d:1348574
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/5/722/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/5/722/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Comte, F. & Renault, E., 1996. "Noncausality in Continuous Time Models," Econometric Theory, Cambridge University Press, vol. 12(2), pages 215-256, June.
    3. Harrison, J. Michael & Pliska, Stanley R., 1983. "A stochastic calculus model of continuous trading: Complete markets," Stochastic Processes and their Applications, Elsevier, vol. 15(3), pages 313-316, August.
    4. S. D. Jacka, 1992. "A Martingale Representation Result and an Application to Incomplete Financial Markets," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 239-250, October.
    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. Timothy Johnson, 2015. "Reciprocity as a Foundation of Financial Economics," Journal of Business Ethics, Springer, vol. 131(1), pages 43-67, September.
    2. N. Azevedo & D. Pinheiro & S. Z. Xanthopoulos & A. N. Yannacopoulos, 2018. "Who would invest only in the risk-free asset?," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-14, September.
    3. Shin-Yun Wang & Ming-Che Chuang & Shih-Kuei Lin & So-De Shyu, 2021. "Option pricing under stock market cycles with jump risks: evidence from the S&P 500 index," Review of Quantitative Finance and Accounting, Springer, vol. 56(1), pages 25-51, January.
    4. Martin Herdegen & Martin Schweizer, 2018. "Semi‐efficient valuations and put‐call parity," Mathematical Finance, Wiley Blackwell, vol. 28(4), pages 1061-1106, October.
    5. Lian, Yu-Min & Chen, Jun-Home, 2022. "Foreign exchange option pricing under regime switching with asymmetrical jumps," Finance Research Letters, Elsevier, vol. 46(PA).
    6. Huhtala, Heli, 2008. "Along but beyond mean-variance: Utility maximization in a semimartingale model," Bank of Finland Research Discussion Papers 5/2008, Bank of Finland.
    7. Martin HERDEGEN & Martin SCHWEIZER, 2016. "Economically Consistent Valuations and Put-Call Parity," Swiss Finance Institute Research Paper Series 16-02, Swiss Finance Institute.
    8. Robert J. Elliott & Tak Kuen Siu, 2016. "Pricing regime-switching risk in an HJM interest rate environment," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1791-1800, December.
    9. repec:dau:papers:123456789/5374 is not listed on IDEAS
    10. Wayne King Ming Chan, 2015. "RAROC-Based Contingent Claim Valuation," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 21, July-Dece.
    11. Lian, Yu-Min & Chen, Jun-Home, 2023. "Valuation of chooser options with state-dependent risks," Finance Research Letters, Elsevier, vol. 52(C).
    12. Abid, Ilyes & Dhaoui, Abderrazak & Goutte, Stéphane & Guesmi, Khaled, 2019. "Contagion and bond pricing: The case of the ASEAN region," Research in International Business and Finance, Elsevier, vol. 47(C), pages 371-385.
    13. Paul McCloud, 2020. "Expectation and Price in Incomplete Markets," Papers 2006.16703, arXiv.org.
    14. repec:zbw:bofrdp:2008_005 is not listed on IDEAS
    15. Alev Meral, 2019. "Comparison of various risk measures for an optimal portfolio," Papers 1912.09573, arXiv.org.
    16. Zhang, Ziqing, 2024. "Multi-regime foreign exchange rate model: Calibration and pricing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 204-218.
    17. Lian, Yu-Min & Chen, Jun-Home & Liao, Szu-Lang, 2021. "Cojump risks and their impacts on option pricing," The Quarterly Review of Economics and Finance, Elsevier, vol. 79(C), pages 399-410.
    18. Hardy Hulley & Thomas A. McWalter, 2015. "Quadratic Hedging of Basis Risk," JRFM, MDPI, vol. 8(1), pages 1-20, February.
    19. Lian, Yu-Min & Chen, Jun-Home, 2020. "Joint dynamic modeling and option pricing in incomplete derivative-security market," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    20. Huhtala, Heli, 2008. "Along but beyond mean-variance : Utility maximization in a semimartingale model," Research Discussion Papers 5/2008, Bank of Finland.
    21. Elyès Jouini & Hédi Kallal, 1999. "Viability and Equilibrium in Securities Markets with Frictions," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 275-292, July.
    22. Lian, Yu-Min & Liao, Szu-Lang & Chen, Jun-Home, 2015. "State-dependent jump risks for American gold futures option pricing," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 115-133.

    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:5:p:722-:d:1348574. 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.