Loss Data Analysis with Maximum Entropy

In book: Mathematical and Statistical Methods for Actuarial Sciences and Finance, Springer. MAF 2018, DOI: 10.1007/978-3-319-89824-7

5 Pages Posted: 27 Apr 2018 Last revised: 3 Nov 2018

See all articles by Erika Gomes-Gonçalves

Erika Gomes-Gonçalves

Independent

Henryk Gzyl

Instituto de Estudios Superiores de Administración (IESA)

Silvia Mayoral Blaya

Universidad Carlos III de Madrid

Date Written: April 7, 2018

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 = ∑ Nn=1 X n , or that of a sum of such random variables. There, N is an integer random variable and then X n are 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.

Keywords: loss distributions, sample dependence, maximum entropy

Suggested Citation

Gomes-Gonçalves, Erika and Gzyl, Henryk and Mayoral Blaya, Silvia, Loss Data Analysis with Maximum Entropy (April 7, 2018). In book: Mathematical and Statistical Methods for Actuarial Sciences and Finance, Springer. MAF 2018, DOI: 10.1007/978-3-319-89824-7. Available at SSRN: https://ssrn.com/abstract=3158218

Erika Gomes-Gonçalves (Contact Author)

Independent ( email )

Madrid
madrid
Madrid, Madrid 28014
Spain

HOME PAGE: http://https://erikapat.github.io/

Henryk Gzyl

Instituto de Estudios Superiores de Administración (IESA) ( email )

Ave, Iesa, San Bernardino
Caracas, 1010
Venezuela

HOME PAGE: http://www.iesa.edu.ve

Silvia Mayoral Blaya

Universidad Carlos III de Madrid ( email )

CL. de Madrid 126
Madrid, Madrid 28903
Spain

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