Upper and Lower Bounds for a Finite-Type Ruin Probability in a Nonhomogeneous Risk Process

Abstract

Based on many numerical examples, Raducan et al. (2015b) stated a conjecture that relates the order in which some nonhomogeneous claims arrive to the magnitude of the corresponding ruin probability. In that conjecture, the usual stochastic order has been considered for the claims. However, in this paper, we prove the conjecture for a different stochastic order, namely the likelihood ratio order. In spite the fact that being stronger, the likelihood order implies the usual stochastic one, for some distributions the two orderings are equivalent, hence our initial conjecture proves to be true in several cases.