IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v164y2020ics0167715220301061.html
   My bibliography  Save this article

Approximating sums of products of dependent random variables

Author

Listed:
  • Gajek, Lesław
  • Krajewska, Elżbieta

Abstract

Stochastic approximation of a given time series {∑j=1kXjYj} by a linear combination of simpler sequences {∑j=1kXj} and {∑j=1kYj} is treated uniformly over k∈{1,…,n}. A maximal inequality is proven in order to find a sharp bound on Value-at-Risk of max1≤k≤n|∑j=1kXjYj|.

Suggested Citation

  • Gajek, Lesław & Krajewska, Elżbieta, 2020. "Approximating sums of products of dependent random variables," Statistics & Probability Letters, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:stapro:v:164:y:2020:i:c:s0167715220301061
    DOI: 10.1016/j.spl.2020.108803
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220301061
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108803?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. Michael J. Brennan & Yihong Xia, 2002. "Dynamic Asset Allocation under Inflation," Journal of Finance, American Finance Association, vol. 57(3), pages 1201-1238, June.
    2. Li, Jinzhu, 2018. "On the joint tail behavior of randomly weighted sums of heavy-tailed random variables," Journal of Multivariate Analysis, Elsevier, vol. 164(C), pages 40-53.
    3. John Y. Campbell & Robert J. Shiller & Luis M. Viceira, 2009. "Understanding Inflation-Indexed Bond Markets," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 40(1 (Spring), pages 79-138.
    4. John Y. Campbell & Robert J. Shiller & Luis M. Viceira, 2009. "Understanding Inflation-Indexed Bond Markets," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 40(1 (Spring), pages 79-138.
    5. Shanchao, Yang, 2006. "Moment inequalities for sums of products of independent random variables," Statistics & Probability Letters, Elsevier, vol. 76(18), pages 1994-2000, December.
    6. Gajek, Lesław & Krajewska, Elżbieta, 2013. "A new immunization inequality for random streams of assets, liabilities and interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 624-631.
    7. Csörgő, Miklós & Nasari, Masoud M., 2013. "Asymptotics of randomly weighted u- and v-statistics: Application to bootstrap," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 176-192.
    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. Cláudia Simões & Luís Oliveira & Jorge M. Bravo, 2021. "Immunization Strategies for Funding Multiple Inflation-Linked Retirement Income Benefits," Risks, MDPI, vol. 9(4), pages 1-28, March.
    2. John Y. Campbell & Robert J. Shiller & Luis M. Viceira, 2009. "Understanding Inflation-Indexed Bond Markets," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 40(1 (Spring), pages 79-138.
    3. Grishchenko, Olesya V. & Vanden, Joel M. & Zhang, Jianing, 2016. "The informational content of the embedded deflation option in TIPS," Journal of Banking & Finance, Elsevier, vol. 65(C), pages 1-26.
    4. Amin, Shehryar & Tédongap, Roméo, 2023. "The changing landscape of treasury auctions," Journal of Banking & Finance, Elsevier, vol. 148(C).
    5. Cartea, Álvaro & Saúl, Jonatan & Toro, Juan, 2012. "Optimal portfolio choice in real terms: Measuring the benefits of TIPS," Journal of Empirical Finance, Elsevier, vol. 19(5), pages 721-740.
    6. Dewachter, Hans & Iania, Leonardo, 2011. "An Extended Macro-Finance Model with Financial Factors," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 46(6), pages 1893-1916, December.
    7. Emi Nakamura & Jón Steinsson & Robert Barro & José Ursúa, 2013. "Crises and Recoveries in an Empirical Model of Consumption Disasters," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(3), pages 35-74, July.
    8. German Gutierrez, 2018. "Investigating Global Labor and Pro t Shares," 2018 Meeting Papers 165, Society for Economic Dynamics.
    9. Hatcher, Michael, 2014. "Indexed versus nominal government debt under inflation and price-level targeting," Journal of Economic Dynamics and Control, Elsevier, vol. 45(C), pages 126-145.
    10. Kajuth, Florian & Watzka, Sebastian, 2011. "Inflation expectations from index-linked bonds: Correcting for liquidity and inflation risk premia," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(3), pages 225-235, June.
    11. Binder, Carola Conces, 2016. "Estimation of historical inflation expectations," Explorations in Economic History, Elsevier, vol. 61(C), pages 1-31.
    12. Michael Hatcher, 2013. "Aggregate and welfare effects of long run inflation risk under inflation and price-level targeting," Working Papers 2013_03, Business School - Economics, University of Glasgow.
    13. Westerhout, Ed & Ciocyte, Ona, 2017. "The Role of Inflation-Linked Bonds. Increasing, but Still Modest," Other publications TiSEM 08878bbd-e76e-4216-bee9-b, Tilburg University, School of Economics and Management.
    14. Kliem, Martin & Meyer-Gohde, Alexander, 2017. "(Un)expected Monetary Policy Shocks and Term Premia," SFB 649 Discussion Papers 2017-015, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    15. Marini, François, 2011. "Financial intermediation in the theory of the risk-free rate," Journal of Banking & Finance, Elsevier, vol. 35(7), pages 1663-1668, July.
    16. Andrea Berardi, 2013. "Inflation Risk Premia, Yield Volatility and Macro Factors," Working Papers 27/2013, University of Verona, Department of Economics.
    17. Westerhout, Ed & Beetsma, Roel, 2019. "A comparison of nominal and indexed debt under fiscal constraints," Journal of International Money and Finance, Elsevier, vol. 91(C), pages 177-194.
    18. Jens H. E. Christensen & Jose A. Lopez & Glenn D. Rudebusch, 2016. "Pricing Deflation Risk with US Treasury Yields," Review of Finance, European Finance Association, vol. 20(3), pages 1107-1152.
    19. Gilbert Cette & Marielle de Jong, 2013. "Breakeven inflation rates and their puzzling correlation relationships," Applied Economics, Taylor & Francis Journals, vol. 45(18), pages 2579-2585, June.
    20. Max Gillman & Michal Kejak & Michal Pakoš, 2015. "Learning about Rare Disasters: Implications For Consumption and Asset Prices," Review of Finance, European Finance Association, vol. 19(3), pages 1053-1104.

    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:stapro:v:164:y:2020:i:c:s0167715220301061. 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/622892/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.