IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v29y2014i5p1187-1205.html
   My bibliography  Save this article

A fast algorithm to sample the number of vertexes and the area of the random convex hull on the unit square

Author

Listed:
  • Chi Ng
  • Johan Lim
  • Kyeong Lee
  • Donghyeon Yu
  • Sujung Choi

Abstract

We propose an algorithm to sample the area of the smallest convex hull containing $$n$$ n sample points uniformly distributed over unit square. To do it, we introduce a new coordinate system for the position of vertexes and re-write joint distribution of the number of vertexes and their locations in the new coordinate system. The proposed algorithm is much faster than existing procedure and has a computational complexity on the order of $$O(T)$$ O ( T ) , where $$T$$ T is the number of vertexes. Using the proposed algorithm, we numerically investigate the asymptotic behavior of functionals of the random convex hull. In addition, we apply it to finding pairs of stocks where the returns are dependent on each other on the New York Stock Exchange. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Chi Ng & Johan Lim & Kyeong Lee & Donghyeon Yu & Sujung Choi, 2014. "A fast algorithm to sample the number of vertexes and the area of the random convex hull on the unit square," Computational Statistics, Springer, vol. 29(5), pages 1187-1205, October.
  • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:1187-1205
    DOI: 10.1007/s00180-014-0486-1
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-014-0486-1
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s00180-014-0486-1?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. Evan Gatev & William N. Goetzmann & K. Geert Rouwenhorst, 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 797-827.
    2. Zani, Sergio & Riani, Marco & Corbellini, Aldo, 1998. "Robust bivariate boxplots and multiple outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 28(3), pages 257-270, September.
    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. Weiguang Han & Boyi Zhang & Qianqian Xie & Min Peng & Yanzhao Lai & Jimin Huang, 2023. "Select and Trade: Towards Unified Pair Trading with Hierarchical Reinforcement Learning," Papers 2301.10724, arXiv.org, revised Feb 2023.
    2. Alessia Naccarato & Andrea Pierini & Giovanna Ferraro, 2021. "Markowitz portfolio optimization through pairs trading cointegrated strategy in long-term investment," Annals of Operations Research, Springer, vol. 299(1), pages 81-99, April.
    3. Khizar Qureshi & Tauhid Zaman, 2024. "Pairs Trading Using a Novel Graphical Matching Approach," Papers 2403.07998, arXiv.org.
    4. Bajgrowicz, Pierre & Scaillet, Olivier, 2012. "Technical trading revisited: False discoveries, persistence tests, and transaction costs," Journal of Financial Economics, Elsevier, vol. 106(3), pages 473-491.
    5. Agarwal, Vikas & Fung, William H. & Loon, Yee Cheng & Naik, Narayan Y., 2004. "Risk and return in convertible arbitrage: Evidence from the convertible bond market," CFR Working Papers 04-03, University of Cologne, Centre for Financial Research (CFR).
    6. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    7. Yang Gao & Stephen Satchell & Nandini Srivastava, 2020. "Styles through a convergent/divergent lens: the curious case of ESG," Journal of Asset Management, Palgrave Macmillan, vol. 21(1), pages 4-12, February.
    8. Qingshuo Song & Qing Zhang, 2013. "An Optimal Pairs-Trading Rule," Papers 1302.6120, arXiv.org.
    9. Bo Liu & Lo-Bin Chang & Hélyette Geman, 2017. "Intraday pairs trading strategies on high frequency data: the case of oil companies," Quantitative Finance, Taylor & Francis Journals, vol. 17(1), pages 87-100, January.
    10. Emmanouil Mavrakis & Christos Alexakis, 2018. "Statistical Arbitrage Strategies under Different Market Conditions: The Case of the Greek Banking Sector," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 17(2), pages 159-185, August.
    11. Bruno Breyer Caldas & João Frois Caldeira & Guilherme Vale Moura, 2016. "Is Pairs Trading Performance Sensitive To The Methodologies?: A Comparison," Anais do XLII Encontro Nacional de Economia [Proceedings of the 42nd Brazilian Economics Meeting] 130, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    12. David S. Sun & Shih-Chuan Tsai & Wei Wang, 2013. "Behavioral Investment Strategy Matters: A Statistical Arbitrage Approach," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 49(S3), pages 47-61, July.
    13. Agarwal, Vikas & Daniel, Naveen D. & Naik, Narayan Y., 2009. "Role of managerial incentives and discretion in hedge fund performance," CFR Working Papers 04-04, University of Cologne, Centre for Financial Research (CFR).
    14. Alexander Shulzhenko, 2023. "Copula-based deviation measure of cointegrated financial assets," Papers 2312.02081, arXiv.org.
    15. James Angel & Douglas McCabe, 2013. "Fairness in Financial Markets: The Case of High Frequency Trading," Journal of Business Ethics, Springer, vol. 112(4), pages 585-595, February.
    16. Oscar Bernal Diaz & Astrid Herinckx & Ariane Szafarz, 2014. "Which short-selling regulation is the least damaging to market efficiency? Evidence from Europe," Post-Print CEB, ULB -- Universite Libre de Bruxelles, vol. 37, pages 244-256, March.
    17. Sayat R. Baronyan & İ. İlkay Boduroğlu & Emrah Şener, 2010. "Investigation Of Stochastic Pairs Trading Strategies Under Different Volatility Regimes," Manchester School, University of Manchester, vol. 78(s1), pages 114-134, September.
    18. Bartram, Söhnke M. & Grinblatt, Mark, 2018. "Agnostic fundamental analysis works," Journal of Financial Economics, Elsevier, vol. 128(1), pages 125-147.
    19. Arjen Siegmann & Denitsa Stefanova, 2011. "Market Liquidity and Exposure of Hedge Funds," Tinbergen Institute Discussion Papers 11-150/2/DSF27, Tinbergen Institute.
    20. Broussard, John Paul & Vaihekoski, Mika, 2012. "Profitability of pairs trading strategy in an illiquid market with multiple share classes," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(5), pages 1188-1201.

    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:spr:compst:v:29:y:2014:i:5:p:1187-1205. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.