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In this paper, a renewal model of risk theory is considered, and relations between tails of the equilibrium distribution of the deficit at the time of ruin and a generalization of the equilibrium distribution of non-ruin are obtained. Extensions to higher order equilibrium distribution and Gerber-Shiu functions are also provided. Distributional properties for Pareto and exponential claims are studied. The results are illustrated by numerical examples.

Relations between integrated tails and moments based on the deficit at ruin in the renewal risk model