The ruin probability of the renewal model with constant interest force and upper-tailed independent heavy-tailed claims
The paper provides a simple formula for the probability of ruin under a special case of the Sparre Andersen risk model where, in addition, interest is earned at a constant force of interest. More precisely, claims are assumed to arrive at random times, which are independent and identically distributed. The sizes of the claims are identically distributed nonnegative random variables that are independent from the interclaim times. It is also assumed that claim sizes follow some heavy-tailed distribution and the dependence between any two claim sizes follows some pre-specified structure. The article's main focus is on the tail distribution of the aggregate claims and on asymptotic properties of the finite-time ruin probability. The explicit expressions that are derived are simple and applicable in any situation where the claim-size distribution is known. As a whole, the paper is clearly written and provides detailed proofs. It relies somewhat on the previous literature on the subject for motivating the research and discussing its outcome. Despite these slight shortcomings, the paper is a pleasant and smooth reading.
scientific article; zbMATH DE number 5816596