A new look at the homogeneous risk model

The present paper aims to revisit the homogeneous risk model investigated by De Vylder and Goovaerts (1999, 2000). First, a claim arrival process is defined on a fixed time interval by assuming that the arrival times satisfy an order statistic property. Then, the variability and the covariance of an aggregate claim amount process is discussed. The distribution of the aggregate discounted claims is also examined. Finally, a closed-form expression for the non-ruin probability is derived in terms of a family of Appell polynomials. This formula holds for all claim distributions, even dependent. It generalizes several results obtained so far.

► We revisit the homogeneous risk model of De Vylder and Goovaerts (1999). ► Claim arrival times are assumed to satisfy an order statistic property. ► The variability and covariance of aggregate claim amounts are discussed. ► An expression for non-ruin probabilities is derived in terms of Appell polynomials.