IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-01103025.html
   My bibliography  Save this paper

Stochastic processes governed by Markovian processes
[Processus stochastiques à incréments Markoviens]

Author

Listed:
  • Lee Dinetan

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

Abstract

We introduce a new class of processes aiming at modelling random fluctuations of an asset value more efficiently than traditional Lévy processes. In this study, we consider that the object value C is a real discrete random process (N → R), whose increments are subject to the present state of a "market", described by a Markovian process M : as the successive market states are not pairwise independent, C's fluctuations are not independent either, so C cannot be assimilated as a Lévy process. We call this structure a C-process : we present methods to analyze it, mainly extending the notion of Lundberg's parameter of a diffusion Lévy process, to take M into account during the computations. Once done, we aim more specifically at controlling C's default time T0 = min ({t ∈ N|C(t)

Suggested Citation

  • Lee Dinetan, 2014. "Stochastic processes governed by Markovian processes [Processus stochastiques à incréments Markoviens]," Working Papers hal-01103025, HAL.
    • Handle: RePEc:hal:wpaper:hal-01103025
    Note: View the original document on HAL open archive server: https://hal.science/hal-01103025
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01103025/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Paulsen, Jostein, 1998. "Sharp conditions for certain ruin in a risk process with stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 135-148, June.
    2. Gerber, Hans U. & Goovaerts, Marc J. & Kaas, Rob, 1987. "On the Probability and Severity of Ruin," ASTIN Bulletin, Cambridge University Press, vol. 17(2), pages 151-163, November.
    3. Timothy C. Johnson, 2002. "Rational Momentum Effects," Journal of Finance, American Finance Association, vol. 57(2), pages 585-608, April.
    4. Cont, Rama & Bouchaud, Jean-Philipe, 2000. "Herd Behavior And Aggregate Fluctuations In Financial Markets," Macroeconomic Dynamics, Cambridge University Press, vol. 4(2), pages 170-196, June.
    5. Delbaen, F. & Haezendonck, J., 1987. "Classical risk theory in an economic environment," Insurance: Mathematics and Economics, Elsevier, vol. 6(2), pages 85-116, April.
    6. Jonathan Lewellen, 2002. "Momentum and Autocorrelation in Stock Returns," The Review of Financial Studies, Society for Financial Studies, vol. 15(2), pages 533-564, March.
    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. Chris Stivers & Licheng Sun, 2013. "Market Cycles and the Performance of Relative Strength Strategies," Financial Management, Financial Management Association International, vol. 42(2), pages 263-290, June.
    2. Tobias Wiest, 2023. "Momentum: what do we know 30 years after Jegadeesh and Titman’s seminal paper?," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 37(1), pages 95-114, March.
    3. Gong, Qiang & Liu, Ming & Liu, Qianqiu, 2015. "Momentum is really short-term momentum," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 169-182.
    4. Sina Ehsani & Juhani T. Linnainmaa, 2019. "Factor Momentum and the Momentum Factor," NBER Working Papers 25551, National Bureau of Economic Research, Inc.
    5. Lesmond, David A. & Schill, Michael J. & Zhou, Chunsheng, 2004. "The illusory nature of momentum profits," Journal of Financial Economics, Elsevier, vol. 71(2), pages 349-380, February.
    6. Goulding, Christian L. & Harvey, Campbell R. & Mazzoleni, Michele G., 2023. "Momentum turning points," Journal of Financial Economics, Elsevier, vol. 149(3), pages 378-406.
    7. Jostein Paulsen, 2008. "Ruin models with investment income," Papers 0806.4125, arXiv.org, revised Dec 2008.
    8. Wang, Jun & Wu, Yangru, 2011. "Risk adjustment and momentum sources," Journal of Banking & Finance, Elsevier, vol. 35(6), pages 1427-1435, June.
    9. Moskowitz, Tobias J. & Ooi, Yao Hua & Pedersen, Lasse Heje, 2012. "Time series momentum," Journal of Financial Economics, Elsevier, vol. 104(2), pages 228-250.
    10. Pan, Li & Tang, Ya & Xu, Jianguo, 2013. "Weekly momentum by return interval ranking," Pacific-Basin Finance Journal, Elsevier, vol. 21(1), pages 1191-1208.
    11. Victor DeMiguel & Francisco J. Nogales & Raman Uppal, 2014. "Stock Return Serial Dependence and Out-of-Sample Portfolio Performance," The Review of Financial Studies, Society for Financial Studies, vol. 27(4), pages 1031-1073.
    12. Chen, Hsiu-Lang & De Bondt, Werner, 2004. "Style momentum within the S&P-500 index," Journal of Empirical Finance, Elsevier, vol. 11(4), pages 483-507, September.
    13. Kim, Junyong, 2024. "Zoom in on momentum," International Review of Financial Analysis, Elsevier, vol. 94(C).
    14. Wahal, Sunil & Yavuz, M. Deniz, 2013. "Style investing, comovement and return predictability," Journal of Financial Economics, Elsevier, vol. 107(1), pages 136-154.
    15. Subrahmanyam, Avanidhar, 2018. "Equity market momentum: A synthesis of the literature and suggestions for future work," Pacific-Basin Finance Journal, Elsevier, vol. 51(C), pages 291-296.
    16. Fernando F. Ferreira & A. Christian Silva & Ju-Yi Yen, 2014. "Information ratio analysis of momentum strategies," Papers 1402.3030, arXiv.org, revised Jul 2014.
    17. Laura Xiaolei Liu & Lu Zhang, 2011. "A Model of Momentum," NBER Working Papers 16747, National Bureau of Economic Research, Inc.
    18. Paulsen, Jostein, 1998. "Ruin theory with compounding assets -- a survey," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 3-16, May.
    19. Li, Kai, 2021. "Nonlinear effect of sentiment on momentum," Journal of Economic Dynamics and Control, Elsevier, vol. 133(C).
    20. Malin, Mirela & Bornholt, Graham, 2010. "Predictability of future index returns based on the 52-week high strategy," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(4), pages 501-508, November.

    More about this item

    Keywords

    Markovian; ruin; default; risk theory; process;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:hal:wpaper:hal-01103025. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.