IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1501.01954.html
   My bibliography  Save this paper

On financial applications of the two-parameter Poisson-Dirichlet distribution

Author

Listed:
  • Sergey Sosnovskiy

Abstract

Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes of mathematical genetics and recently applied in non-parametric Bayesian statistics, provides probabilistic-combinatorial approach for analysis and modeling of the capital distribution curve. Framework of the two-parameter Poisson-Dirichlet distribution contains rich set of methods and tools, including infinite-dimensional diffusion process. The purpose of this note is to introduce framework of exchangeable distributions on partitions in the financial context. In particular, it is shown that averaged samples from the Poisson-Dirichlet distribution provide approximation to the capital distribution curves in equity markets. This suggests that the two-parameter model can be employed for modelling evolution of market weights and prices fluctuating in stochastic equilibrium.

Suggested Citation

  • Sergey Sosnovskiy, 2015. "On financial applications of the two-parameter Poisson-Dirichlet distribution," Papers 1501.01954, arXiv.org, revised Jul 2015.
    • Handle: RePEc:arx:papers:1501.01954
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1501.01954
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Masanao Aoki, 2003. "Applications of Exchangeable Random Partitions to Economic Modeling," UCLA Economics Online Papers 228, UCLA Department of Economics.
    2. Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Annals of Finance, Springer, vol. 9(3), pages 439-454, August.
    3. Garibaldi,Ubaldo & Scalas,Enrico, 2010. "Finitary Probabilistic Methods in Econophysics," Cambridge Books, Cambridge University Press, number 9780521515597, September.
    4. U. Garibaldi & D. Costantini & P. Viarengo, 2007. "The two-parameter Ewens distribution: a finitary approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 2(2), pages 147-161, December.
    5. Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Papers 1302.3870, arXiv.org.
    6. Masanao Aoki, 2001. "Modeling Aggregate Behavior and Fluctuations in Economics: Stochastic Views of Interacting Agents," UCLA Economics Online Papers 142, UCLA Department of Economics.
    7. Aoki,Masanao, 2004. "Modeling Aggregate Behavior and Fluctuations in Economics," Cambridge Books, Cambridge University Press, number 9780521606196, September.
    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. Dassios, Angelos & Zhang, Junyi, 2021. "Exact simulation of two-parameter Poisson-Dirichlet random variables," LSE Research Online Documents on Economics 107937, London School of Economics and Political Science, LSE Library.
    2. Eric Andr'e & Guillaume Coqueret, 2020. "Dirichlet policies for reinforced factor portfolios," Papers 2011.05381, arXiv.org, revised Jun 2021.

    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. Sergey Sosnovskiy, 2015. "Market shape formation, statistical equilibrium and neutral evolution theory," Papers 1506.07163, arXiv.org.
    2. Scalas, Enrico & Gallegati, Mauro & Guerci, Eric & Mas, David & Tedeschi, Alessandra, 2006. "Growth and allocation of resources in economics: The agent-based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 86-90.
    3. Roman, Mihai Daniel, 2008. "Entreprises behavior in cooperative and punishment‘s repeated negotiations," MPRA Paper 37527, University Library of Munich, Germany, revised 05 Jan 2009.
    4. Ali Al-Aradi & Sebastian Jaimungal, 2019. "Active and Passive Portfolio Management with Latent Factors," Papers 1903.06928, arXiv.org.
    5. David Itkin & Martin Larsson, 2024. "Calibrated rank volatility stabilized models for large equity markets," Papers 2403.04674, arXiv.org.
    6. Roman, Mihai Daniel, 2010. "A game theoretic approach of war with financial influences," MPRA Paper 38389, University Library of Munich, Germany.
    7. U. Garibaldi & P. Viarengo, 2012. "Exchangeability and non-self-averaging," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(2), pages 181-195, October.
    8. Benjamin Jourdain & Julien Reygner, 2015. "Capital distribution and portfolio performance in the mean-field Atlas model," Post-Print hal-00921151, HAL.
    9. Steven Campbell & Qien Song & Ting-Kam Leonard Wong, 2024. "Macroscopic properties of equity markets: stylized facts and portfolio performance," Papers 2409.10859, arXiv.org, revised Oct 2024.
    10. Benjamin Jourdain & Julien Reygner, 2013. "Capital distribution and portfolio performance in the mean-field Atlas model," Papers 1312.5660, arXiv.org, revised Aug 2014.
    11. Jalali-Naini , Ahmad. R. & Hemati , Maryam, 2012. "The Effect of Monetary Shocks on Disaggregated Prices in a Data Rich Environment: a Bayesian FAVAR Approach," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 6(4), pages 27-60, July.
    12. Kangjianan Xie, 2020. "Leakage of rank-dependent functionally generated trading strategies," Annals of Finance, Springer, vol. 16(4), pages 573-591, December.
    13. Alexander Vervuurt, 2015. "Topics in Stochastic Portfolio Theory," Papers 1504.02988, arXiv.org.
    14. Enrico Scalas & Tijana Radivojević & Ubaldo Garibaldi, 2015. "Wealth distribution and the Lorenz curve: a finitary approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 10(1), pages 79-89, April.
    15. Aoki, Masanao, 2002. "Open models of share markets with two dominant types of participants," Journal of Economic Behavior & Organization, Elsevier, vol. 49(2), pages 199-216, October.
    16. David Vidal-Tomás & Simone Alfarano, 2020. "An agent-based early warning indicator for financial market instability," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(1), pages 49-87, January.
    17. Bertram During & Nicos Georgiou & Enrico Scalas, 2016. "A stylized model for wealth distribution," Papers 1609.08978, arXiv.org, revised Jul 2021.
    18. Ellis Scharfenaker, 2022. "Statistical Equilibrium Methods In Analytical Political Economy," Journal of Economic Surveys, Wiley Blackwell, vol. 36(2), pages 276-309, April.
    19. Charles D. Brummitt & Kenan Huremović & Paolo Pin & Matthew H. Bonds & Fernando Vega-Redondo, 2017. "Contagious disruptions and complexity traps in economic development," Nature Human Behaviour, Nature, vol. 1(9), pages 665-672, September.

    More about this item

    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:arx:papers:1501.01954. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.