Random sums of exchangeable variables and actuarial applications

In this paper we study the accumulated claim in some fixed time period, skipping the classical assumption of mutual independence between the variables involved. Two basic models are considered: Model 1 assumes that any pair of claims are equally correlated which means that the corresponding square-integrable sequence is exchangeable one. Model 2 states that the correlations between the adjacent claims are the same. Recurrence and explicit expressions for the joint probability generating function are derived and the impact of the dependence parameter (correlation coefficient) in both models is examined. The Markov binomial distribution is obtained as a particular case under assumptions of Model 2.