APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY Appl. Stochastic Models Bus. Ind. 2010; 26:737–757 Published online 27 November 2009 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/asmb.814 Exchangeable claim sizes in a compound Poisson-type process Rams´ es H. Mena 1 and Luis E. Nieto-Barajas 2, ∗, † 1 Department of Probability and Statistics, IIMAS–UNAM, Mexico 2 Department of Statistics, ITAM, Mexico SUMMARY 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 partic- ular, 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. Received 26 March 2009; Revised 6 August 2009; Accepted 19 August 2009 KEY WORDS: Bayesian nonparametric analysis; compound Poisson process; exchangeable claim process; exchangeable sequence; panel data; risk model 1. INTRODUCTION In insurance and risk modeling, the study of the dynamics through time of the wealth of a business has been an object of research for several decades. In the basic setup of collective risk theory, the interest lies in the probability distribution of the reserve process and, henceforth, using historical information and a robust model, in predicting potential bankruptcies. The cornerstone tool is based on the modeling of the aggregated claims’ amount through the compound Poisson process (CPP), ∗ Correspondence to: Luis E. Nieto-Barajas, ITAM, Rio Hondo 1, Progreso Tizapan, 01080 Mexico, D.F. † E-mail: lnieto@itam.mx Contract/grant sponsor: National Council for Science and National Technology of Mexico (CONACYT); contract/grant numbers: J48072-F, J50160-F Contract/grant sponsor: ICER, Turin Copyright 2009 John Wiley & Sons, Ltd.