IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v25y2023i3d10.1007_s11009-023-10041-2.html
   My bibliography  Save this article

A Versatile Stochastic Dissemination Model

Author

Listed:
  • K. M. D. Chan

    (Korteweg-de Vries Institute, University of Amsterdam
    Transtrend BV)

  • M. R. H. Mandjes

    (Korteweg-de Vries Institute, University of Amsterdam)

Abstract

This paper considers a highly general dissemination model that keeps track of the stochastic evolution of the distribution of wealth over a set of agents. There are two types of events: (i) units of wealth externally arrive, and (ii) units of wealth are redistributed among the agents, while throughout Markov modulation is allowed. We derive a system of coupled differential equations describing the joint transient distribution of the agents’ wealth values, which translate into linear differential equations when considering the corresponding means and (co-)variances. While our model uses the (economic) terminology of wealth being distributed over agents, we illustrate through a series of examples that it can be used considerably more broadly. Indeed, it also facilitates the analysis of the spread of opinions over a population (thus generalizing existing opinion dynamics models), and the analysis of the dynamics of a file storage system (thus allowing the assessment of the efficacy of storage policies).

Suggested Citation

  • K. M. D. Chan & M. R. H. Mandjes, 2023. "A Versatile Stochastic Dissemination Model," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-25, September.
  • Handle: RePEc:spr:metcap:v:25:y:2023:i:3:d:10.1007_s11009-023-10041-2
    DOI: 10.1007/s11009-023-10041-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-023-10041-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11009-023-10041-2?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. Ghislain Léveillé & José Garrido, 2001. "Recursive Moments of Compound Renewal Sums with Discounted Claims," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2001(2), pages 98-110.
    2. O. J. Boxma & E. J. Cahen & D. Koops & M. Mandjes, 2019. "Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 125-153, March.
    3. Leveille, Ghislain & Garrido, Jose, 2001. "Moments of compound renewal sums with discounted claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 217-231, April.
    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. Wu, Yang-Che & Chung, San-Lin, 2010. "Catastrophe risk management with counterparty risk using alternative instruments," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 234-245, October.
    2. Zhang, Zhehao, 2018. "Renewal sums under mixtures of exponentials," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 281-301.
    3. Ghislain Léveillé & Emmanuel Hamel, 2018. "Conditional, Non-Homogeneous and Doubly Stochastic Compound Poisson Processes with Stochastic Discounted Claims," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 353-368, March.
    4. Daniel J. Geiger & Akim Adekpedjou, 2022. "Analysis of IBNR Liabilities with Interevent Times Depending on Claim Counts," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 815-829, June.
    5. Jang, Jiwook, 2007. "Jump diffusion processes and their applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 62-70, July.
    6. Angelos Dassios & Jiwook Jang & Hongbiao Zhao, 2019. "A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance," Risks, MDPI, vol. 7(4), pages 1-18, October.
    7. Woo, Jae-Kyung, 2016. "On multivariate discounted compound renewal sums with time-dependent claims in the presence of reporting/payment delays," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 354-363.
    8. Castañer, A. & Claramunt, M.M. & Lefèvre, C. & Loisel, S., 2015. "Discrete Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 343-362.
    9. Cheung, Eric C.K., 2013. "Moments of discounted aggregate claim costs until ruin in a Sparre Andersen risk model with general interclaim times," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 343-354.
    10. Jang, Jiwook & Dassios, Angelos & Zhao, Hongbiao, 2018. "Moments of renewal shot-noise processes and their applications," LSE Research Online Documents on Economics 87428, London School of Economics and Political Science, LSE Library.
    11. Cossette, Hélène & Landriault, David & Marceau, Etienne & Moutanabbir, Khouzeima, 2012. "Analysis of the discounted sum of ascending ladder heights," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 393-401.
    12. Zhang, Zhehao, 2019. "On the stochastic equation L(Z)=L[V(X+Z)] and properties of Mittag–Leffler distributions," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 365-376.
    13. Marri, Fouad & Furman, Edward, 2012. "Pricing compound Poisson processes with the Farlie–Gumbel–Morgenstern dependence structure," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 151-157.
    14. Hyunjoo Yoo & Bara Kim & Jeongsim Kim & Jiwook Jang, 2020. "Transform approach for discounted aggregate claims in a risk model with descendant claims," Annals of Operations Research, Springer, vol. 293(1), pages 175-192, October.
    15. Ya Fang Wang & José Garrido & Ghislain Léveillé, 2018. "The Distribution of Discounted Compound PH–Renewal Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 69-96, March.
    16. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2019. "A generalised CIR process with externally-exciting and self-exciting jumps and its applications in insurance and finance," LSE Research Online Documents on Economics 102043, London School of Economics and Political Science, LSE Library.
    17. Ren, Jiandong, 2012. "A multivariate aggregate loss model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 402-408.
    18. Siti Norafidah Mohd Ramli & Jiwook Jang, 2014. "Neumann Series on the Recursive Moments of Copula-Dependent Aggregate Discounted Claims," Risks, MDPI, vol. 2(2), pages 1-16, May.
    19. Jang, Ji-Wook & Krvavych, Yuriy, 2004. "Arbitrage-free premium calculation for extreme losses using the shot noise process and the Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 35(1), pages 97-111, August.
    20. Kim, Bara & Kim, Hwa-Sung, 2007. "Moments of claims in a Markovian environment," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 485-497, May.

    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:metcap:v:25:y:2023:i:3:d:10.1007_s11009-023-10041-2. 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.