IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-319-89824-7_70.html

Loss Data Analysis with Maximum Entropy

In: Mathematical and Statistical Methods for Actuarial Sciences and Finance

Author

Listed:
  • Erika Gomes-Gonçalves

    (Independent Consultant)

  • Henryk Gzyl

    (Instituto de Estudios Superiores de Administración - IESA)

  • Silvia Mayoral

    (Department of Business Administration, Univ. Carlos III, Madrid)

Abstract

We present some results of the application of maximum entropy methods to determine the probability density of compound random variables. This problem is very important in the banking and insurance business, but also appears in system reliability and in operations research. The mathematical tool consists of inverting Laplace transforms of positive compound random variables using the maximum entropy method. This method needs a very small number of (real) values of the Laplace transform, is robust, works with small data sets, and it can be extended to include errors in the data as well as data specified up to intervals. In symbols, the basic typical problem consist in determining the density f S of a compound random variable like S = ∑ n = 1 N X n $$S = \sum _{n=1}^N X_n$$ , or that of a sum of such random variables. There, N is an integer random variable and X n is a sequence of positive, continuous random variables, independent among themselves and of N. Our methodology can be applied to determine the probability density of the total loss S and that of the individual losses.

Suggested Citation

  • Erika Gomes-Gonçalves & Henryk Gzyl & Silvia Mayoral, 2018. "Loss Data Analysis with Maximum Entropy," Springer Books, in: Marco Corazza & María Durbán & Aurea Grané & Cira Perna & Marilena Sibillo (ed.), Mathematical and Statistical Methods for Actuarial Sciences and Finance, pages 391-395, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-89824-7_70
    DOI: 10.1007/978-3-319-89824-7_70
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;

    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:spr:sprchp:978-3-319-89824-7_70. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.