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Exchangeable claim sizes in a compound Poisson‐type process
Author(s) -
Mena Ramsés H.,
NietoBarajas Luis E.
Publication year - 2010
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.814
Subject(s) - independence (probability theory) , poisson distribution , conditional independence , econometrics , medical expenditure panel survey , compound poisson process , type (biology) , nonparametric statistics , mathematics , marginal distribution , parametric statistics , compound poisson distribution , panel data , mathematical economics , statistics , economics , poisson process , poisson regression , random variable , ecology , health care , population , demography , sociology , health insurance , biology , economic growth
Abstract When dealing with risk models the typical assumption of independence among claim size distributions is not always satisfied. Here we consider the case when the claim sizes are exchangeable and study the implications when constructing aggregated claims through compound Poisson‐type processes. In particular, exchangeability is achieved through conditional independence, using parametric and nonparametric measures for the conditioning distribution. Bayes' theorem is employed to ensure an arbitrary but fixed marginal distribution for the claim sizes. A full Bayesian analysis of the proposed model is illustrated with a panel‐type data set coming from a Medical Expenditure Panel Survey (MEPS). Copyright © 2009 John Wiley & Sons, Ltd.