IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v91y2020icp166-187.html
   My bibliography  Save this article

Copula-based Markov process

Author

Listed:
  • Fang, Jun
  • Jiang, Fan
  • Liu, Yong
  • Yang, Jingping

Abstract

Starting from a bivariate copula family, this paper investigates the existence of a Markov process whose temporal dependence is modeled by the given copula family. Due to that the transition function plays a core role for constructing a Markov process, a transition function should be defined from a copula family. For this purpose, the modified partial Dini derivatives of a bivariate copula are defined and applied for defining transition probabilities, and some properties of the modified partial Dini derivatives are proved. A necessary and sufficient condition for the family of the defined transition probabilities to be a transition function is provided. Given a bivariate copula family, a sufficient condition for the existence of a Markov process is provided, where the Markov process has a transition function generated by the modified partial Dini derivatives of the bivariate copula family and the temporal dependence of the Markov process is modeled by the given copula family. The resulting Markov process is named as the copula-based Markov process. Moreover, under some assumptions the consistency of the bivariate copula family under the ∗ product operation is necessary and sufficient for the existence of a Markov process. In terms of copulas, some criteria are provided for a copula-based Markov process to be path right-continuous with left limits or path continuous, and a necessary and sufficient condition for a time-homogeneous copula-based Markov process to be a Feller process is obtained. It is interesting that a Markov process with the transition function generated by the modified partial Dini derivatives of FGM copulas is not a Feller process. Finally, paths of some typical copula-based Markov processes are simulated to show the importance of fitting the copula method into the framework of stochastic processes.

Suggested Citation

  • Fang, Jun & Jiang, Fan & Liu, Yong & Yang, Jingping, 2020. "Copula-based Markov process," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 166-187.
    • Handle: RePEc:eee:insuma:v:91:y:2020:i:c:p:166-187
    DOI: 10.1016/j.insmatheco.2020.01.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668720300147
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2020.01.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. repec:oup:rfinst:v:25:y::i:12:p:3711-3751 is not listed on IDEAS
    2. Rob Kaas & Marc Goovaerts & Jan Dhaene & Michel Denuit, 2008. "Modern Actuarial Risk Theory," Springer Books, Springer, edition 2, number 978-3-540-70998-5, February.
    3. Dong Hwan Oh & Andrew J. Patton, 2018. "Time-Varying Systemic Risk: Evidence From a Dynamic Copula Model of CDS Spreads," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 181-195, April.
    4. Rustam Ibragimov, 2005. "Copula-Based Dependence Characterizations and Modeling for Time Series," Harvard Institute of Economic Research Working Papers 2094, Harvard - Institute of Economic Research.
    5. Beare, Brendan K., 2012. "Archimedean Copulas And Temporal Dependence," Econometric Theory, Cambridge University Press, vol. 28(6), pages 1165-1185, December.
    6. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2015. "Density approach in modelling successive defaults," Post-Print hal-00870492, HAL.
    7. Kaas, Rob & Laeven, Roger J.A. & Nelsen, Roger B., 2009. "Worst VaR scenarios with given marginals and measures of association," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 146-158, April.
    8. Kakouris, Iakovos & Rustem, Berç, 2014. "Robust portfolio optimization with copulas," European Journal of Operational Research, Elsevier, vol. 235(1), pages 28-37.
    9. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    10. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    11. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, January.
    12. Peter Christoffersen & Vihang Errunza & Kris Jacobs & Hugues Langlois, 2012. "Is the Potential for International Diversification Disappearing? A Dynamic Copula Approach," The Review of Financial Studies, Society for Financial Studies, vol. 25(12), pages 3711-3751.
    13. Choroś-Tomczyk, Barbara & Härdle, Wolfgang Karl & Okhrin, Ostap, 2013. "Valuation of collateralized debt obligations with hierarchical Archimedean copulae," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 42-62.
    14. Ibragimov, Rustam, 2009. "Copula-Based Characterizations For Higher Order Markov Processes," Econometric Theory, Cambridge University Press, vol. 25(3), pages 819-846, June.
    15. Beare, Brendan K. & Seo, Juwon, 2014. "Time Irreversible Copula-Based Markov Models," Econometric Theory, Cambridge University Press, vol. 30(5), pages 923-960, October.
    16. Trutschnig, Wolfgang, 2013. "On Cesáro convergence of iterates of the star product of copulas," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 357-365.
    17. Juan Fernández Sánchez & Wolfgang Trutschnig, 2016. "Some members of the class of (quasi-)copulas with given diagonal from the Markov kernel perspective," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1508-1526, March.
    18. Enrico Bibbona & Laura Sacerdote & Emiliano Torre, 2016. "A Copula-Based Method to Build Diffusion Models with Prescribed Marginal and Serial Dependence," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 765-783, September.
    19. Achal Bassamboo & Sandeep Juneja & Assaf Zeevi, 2008. "Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation," Operations Research, INFORMS, vol. 56(3), pages 593-606, June.
    20. Ballotta, Laura & Haberman, Steven, 2006. "The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 195-214, February.
    21. Yang, Jingping & Cheng, Shihong & Zhang, Lihong, 2006. "Bivariate copula decomposition in terms of comonotonicity, countermonotonicity and independence," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 267-284, October.
    22. Ahmadi, Seyed Saeed & Gaillardetz, Patrice, 2015. "Modeling mortality and pricing life annuities with Lévy processes," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 337-350.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wiesberg, Igor Lapenda & de Medeiros, José Luiz & Paes de Mello, Raphael V. & Santos Maia, Jeiveison G.S. & Bastos, João Bruno V. & Araújo, Ofélia de Queiroz F., 2021. "Bioenergy production from sugarcane bagasse with carbon capture and storage: Surrogate models for techno-economic decisions," Renewable and Sustainable Energy Reviews, Elsevier, vol. 150(C).
    2. Wang, Fan & Li, Heng & Dong, Chao, 2021. "Understanding near-miss count data on construction sites using greedy D-vine copula marginal regression," Reliability Engineering and System Safety, Elsevier, vol. 213(C).

    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. Juwon Seo, 2018. "Randomization Tests for Equality in Dependence Structure," Papers 1811.02105, arXiv.org.
    2. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    3. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    4. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    5. Brendan K. Beare & Juwon Seo, 2015. "Vine Copula Specifications for Stationary Multivariate Markov Chains," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(2), pages 228-246, March.
    6. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Estimating non-linear serial and cross-interdependence between financial assets," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 837-846.
    7. Rubén Loaiza‐Maya & Michael S. Smith & Worapree Maneesoonthorn, 2018. "Time series copulas for heteroskedastic data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 332-354, April.
    8. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    9. Xiaohong Chen & Zhijie Xiao & Bo Wang, 2020. "Copula-Based Time Series With Filtered Nonstationarity," Cowles Foundation Discussion Papers 2242R, Cowles Foundation for Research in Economics, Yale University, revised Oct 2020.
    10. Smith, Michael Stanley, 2015. "Copula modelling of dependence in multivariate time series," International Journal of Forecasting, Elsevier, vol. 31(3), pages 815-833.
    11. Ouyang, Ruolan & Chen, Xiang & Fang, Yi & Zhao, Yang, 2022. "Systemic risk of commodity markets: A dynamic factor copula approach," International Review of Financial Analysis, Elsevier, vol. 82(C).
    12. Yang Zhao & Charalampos Stasinakis & Georgios Sermpinis & Filipa Da Silva Fernandes, 2019. "Revisiting Fama–French factors' predictability with Bayesian modelling and copula‐based portfolio optimization," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 24(4), pages 1443-1463, October.
    13. Nagler, Thomas & Krüger, Daniel & Min, Aleksey, 2022. "Stationary vine copula models for multivariate time series," Journal of Econometrics, Elsevier, vol. 227(2), pages 305-324.
    14. Chen, Xiaohong & Xiao, Zhijie & Wang, Bo, 2022. "Copula-based time series with filtered nonstationarity," Journal of Econometrics, Elsevier, vol. 228(1), pages 127-155.
    15. Peter Christoffersen & Kris Jacobs & Xisong Jin & Hugues Langlois, 2013. "Dynamic Diversification in Corporate Credit," CREATES Research Papers 2013-46, Department of Economics and Business Economics, Aarhus University.
    16. Bladt Martin & McNeil Alexander J., 2022. "Time series with infinite-order partial copula dependence," Dependence Modeling, De Gruyter, vol. 10(1), pages 87-107, January.
    17. Fermanian, Jean-David & Wegkamp, Marten H., 2012. "Time-dependent copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 19-29.
    18. Tachibana, Minoru, 2022. "Safe haven assets for international stock markets: A regime-switching factor copula approach," Research in International Business and Finance, Elsevier, vol. 60(C).
    19. Oleg Sokolinskiy & Dick van Dijk, 2011. "Forecasting Volatility with Copula-Based Time Series Models," Tinbergen Institute Discussion Papers 11-125/4, Tinbergen Institute.
    20. Azam, Kazim & Pitt, Michael, 2014. "Bayesian Inference for a Semi-Parametric Copula-based Markov Chain," The Warwick Economics Research Paper Series (TWERPS) 1051, University of Warwick, Department of Economics.

    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:eee:insuma:v:91:y:2020:i:c:p:166-187. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    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.