IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v127y2017i4p1125-1170.html
   My bibliography  Save this article

Conditional Markov chains: Properties, construction and structured dependence

Author

Listed:
  • Bielecki, Tomasz R.
  • Jakubowski, Jacek
  • Niewęgłowski, Mariusz

Abstract

In this paper we contribute to the theory of conditional Markov chains (CMCs) that take finitely many values and that admit intensity. We provide a method for constructing a CMC with given intensity and with given conditional initial law, and which is also a doubly stochastic Markov chain. We provide a martingale characterization for such process, and we discuss other useful properties. We define and give sufficient and necessary conditions for strong Markovian consistency and weak Markovian consistency of a multivariate CMC. We use these results to model structured dependence between univariate CMCs, that is, to model a multivariate CMC whose components are univariate CMCs with given laws. An example of potential application of our theory is presented.

Suggested Citation

  • Bielecki, Tomasz R. & Jakubowski, Jacek & Niewęgłowski, Mariusz, 2017. "Conditional Markov chains: Properties, construction and structured dependence," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1125-1170.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:4:p:1125-1170
    DOI: 10.1016/j.spa.2016.07.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414916301223
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2016.07.010?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. Ernst Eberlein & Fehmi Özkan, 2003. "The Defaultable Lévy Term Structure: Ratings and Restructuring," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 277-300, April.
    2. Tomasz R. Bielecki & Marek Rutkowski, 2000. "Multiple Ratings Model of Defaultable Term Structure," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 125-139, April.
    3. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-438, July.
    4. Amendinger, Jürgen, 2000. "Martingale representation theorems for initially enlarged filtrations," Stochastic Processes and their Applications, Elsevier, vol. 89(1), pages 101-116, September.
    5. Bielecki, Tomasz R. & Jakubowski, Jacek & Niewȩgłowski, Mariusz, 2012. "Study of dependence for some stochastic processes: Symbolic Markov copulae," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 930-951.
    6. Biagini, Francesca & Groll, Andreas & Widenmann, Jan, 2013. "Intensity-based premium evaluation for unemployment insurance products," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 302-316.
    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. Edward Hoyle & Levent Ali Menguturk, 2020. "Generalised Liouville Processes and their Properties," Papers 2003.11312, arXiv.org, revised May 2020.
    2. Budhi Surya, 2021. "A new class of conditional Markov jump processes with regime switching and path dependence: properties and maximum likelihood estimation," Papers 2107.07026, arXiv.org.
    3. Tomasz R. Bielecki & Igor Cialenco & Shibi Feng, 2018. "A Dynamic Model Of Central Counterparty Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-34, December.

    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. Emeka Nkoro & Aham Kelvin Uko, 2016. "Exchange Rate and Inflation Volatility and Stock Prices Volatility: Evidence from Nigeria, 1986-2012," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 6(6), pages 1-4.
    2. Czujack, Corinna & Flôres Junior, Renato Galvão & Ginsburgh, Victor, 1995. "On long-run price comovements between paintings and prints," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 269, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    3. Sotirios Varelas, 2022. "Virtual Immersive Platforms as a Strategic Innovative Destination Marketing Tool in the COVID-19 Era," Sustainability, MDPI, vol. 14(19), pages 1-15, October.
    4. Loperfido, Nicola, 2010. "A note on marginal and conditional independence," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1695-1699, December.
    5. Hyunsoo Kang, 2022. "Impacts of Income Inequality and Economic Growth on CO 2 Emissions: Comparing the Gini Coefficient and the Top Income Share in OECD Countries," Energies, MDPI, vol. 15(19), pages 1-15, September.
    6. KAMKOUM, Arnaud Cedric, 2023. "The Federal Reserve’s Response to the Global Financial Crisis and its Effects: An Interrupted Time-Series Analysis of the Impact of its Quantitative Easing Programs," Thesis Commons d7pvg, Center for Open Science.
    7. Bierens, H.J. & Broersma, L., 1991. "The relation between unemployment and interest rate : some international evidence," Serie Research Memoranda 0112, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    8. Zamani, Mehrzad, 2007. "Energy consumption and economic activities in Iran," Energy Economics, Elsevier, vol. 29(6), pages 1135-1140, November.
    9. Jumah, Adusei & Kunst, Robert M., 2001. "The Effects of Exchange-Rate Exposures on Equity Asset Markets," Economics Series 94, Institute for Advanced Studies.
    10. Muhammad Shafiullah & Ravinthirakumaran Navaratnam, 2016. "Do Bangladesh and Sri Lanka Enjoy Export-Led Growth? A Comparison of Two Small South Asian Economies," South Asia Economic Journal, Institute of Policy Studies of Sri Lanka, vol. 17(1), pages 114-132, March.
    11. Portes, Richard & Santorum, Anita, 1987. "Money and the consumption goods market in China," Journal of Comparative Economics, Elsevier, vol. 11(3), pages 354-371, September.
    12. Alberto Fuertes & Simón Sosvilla-Rivero, 2019. "“Forecasting emerging market currencies: Are inflation expectations useful?”," IREA Working Papers 201918, University of Barcelona, Research Institute of Applied Economics, revised Oct 2019.
    13. Diana Ricciulli-Marín, 2020. "The Fiscal Cost of Conflict: Evidence from La Violencia in Colombia," Cuadernos de Historia Económica 53, Banco de la Republica de Colombia.
    14. Wesam Salah Alaloul & Muhammad Ali Musarat & Muhammad Babar Ali Rabbani & Qaiser Iqbal & Ahsen Maqsoom & Waqas Farooq, 2021. "Construction Sector Contribution to Economic Stability: Malaysian GDP Distribution," Sustainability, MDPI, vol. 13(9), pages 1-26, April.
    15. Xiaojie Xu, 2017. "The rolling causal structure between the Chinese stock index and futures," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 31(4), pages 491-509, November.
    16. Hany Eldemerdash & Hugh Metcalf & Sara Maioli, 2014. "Twin deficits: new evidence from a developing (oil vs. non-oil) countries’ perspective," Empirical Economics, Springer, vol. 47(3), pages 825-851, November.
    17. Olivier Damette & Stéphane Goutte, 2021. "Weather, Pollution, and Covid-19 Spread: A Time Series and Wavelet Reassessment," Springer Books, in: Fateh Belaïd & Anna Cretì (ed.), Energy Transition, Climate Change, and COVID-19, pages 95-106, Springer.
    18. Ibrahim Ari & Muammer Koc, 2018. "Sustainable Financing for Sustainable Development: Understanding the Interrelations between Public Investment and Sovereign Debt," Sustainability, MDPI, vol. 10(11), pages 1-25, October.
    19. H. Gonca DÝLER & F.Çiðdem TARHAN, 2015. "The Relationship Between Current Account Deficit Budget Deficit: A Research On Turkey," Eurasian Business & Economics Journal, Eurasian Academy Of Sciences, vol. 2(2), pages 24-36, July.
    20. ?ikolaos A. Kyriazis, 2021. "Impacts of Stock Indices, Oil, and Twitter Sentiment on Major Cryptocurrencies during the COVID-19 First Wave," Bulletin of Applied Economics, Risk Market Journals, vol. 8(2), pages 133-146.

    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:spapps:v:127:y:2017:i:4:p:1125-1170. 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/wps/find/journaldescription.cws_home/505572/description#description .

    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.