# The net Bayes premium with dependence between the risk profiles

*A. Hernández-Bastida*,
*Pilar Fernandez-Sanchez* () and
*E. Gómez-Déniz*

Authors registered in the RePEc Author Service: *Hernández-Bastida Agustín* ()

*Insurance: Mathematics and Economics*, 2009, vol. 45, issue 2, 247-254

**Abstract:**
In Bayesian analysis it is usual to assume that the risk profiles [Theta]1 and [Theta]2 associated with the random variables "number of claims" and "amount of a single claim", respectively, are independent. A few studies have addressed a model of this nature assuming some degree of dependence between the two random variables (and most of these studies include copulas). In this paper, we focus on the collective and Bayes net premiums for the aggregate amount of claims under a compound model assuming some degree of dependence between the random variables [Theta]1 and [Theta]2. The degree of dependence is modelled using the Sarmanov-Lee family of distributions [Sarmanov, O.V., 1966. Generalized normal correlation and two-dimensional Frechet classes. Doklady (Soviet Mathematics) 168, 596-599 and Ting-Lee, M.L., 1996. Properties and applications of the Sarmanov family of bivariate distributions. Communications Statistics: Theory and Methods 25 (6) 1207-1222], which allows us to study the impact of this assumption on the collective and Bayes net premiums. The results obtained show that a low degree of correlation produces Bayes premiums that are highly sensitive.

**Keywords:** Bayes; Collective; risk; model; Dependence; Net; premium; Risk; profile (search for similar items in EconPapers)

**Date:** 2009

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0167-6687(09)00080-8

Full text for ScienceDirect subscribers only

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:insuma:v:45:y:2009:i:2:p:247-254

Access Statistics for this article

Insurance: Mathematics and Economics is currently edited by *R. Kaas*, *Hansjoerg Albrecher*, *M. J. Goovaerts* and *E. S. W. Shiu*

More articles in Insurance: Mathematics and Economics from Elsevier

Bibliographic data for series maintained by Catherine Liu ().