On a conjecture related to the ruin probability for nonhomogeneous insurance claims

Recently, nonhomogeneous claim sizes have been considered in the actuarial literature starting from the fact that the claims are seasonally influenced by the economic environment. In this context, Raducan et al. [8] obtained recursive formulas for the ruin probability at or before claim instants, and stated a conjecture that relates the order of the claims arrival to the magnitude of the corresponding ruin probability, conjecture supported by numerical examples. In this paper, we prove this conjecture in a particular case.