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In ruin theory, the net profit condition intuitively means that the incurredrandom claims on average do not occur more often than premiums are gained. Thebreach of the net profit condition causes guaranteed ruin in few but simplecases when both the claims' inter-occurrence time and random claims aredegenerate. In this work, we give a simplified argumentation for theunavoidable ruin when the incurred claims on average occur equally as thepremiums are gained. We study the discrete-time risk model with$N\in\mathbb{N}$ periodically occurring independent distributions, theclassical risk model, also known as the Cram\'er-Lundberg risk process, and themore general E. Sparre Andersen model.

Ruin probability for renewal risk models with neutral net profit condition