The proper distribution function of the deficit in the delayed renewal risk model

The main focus of this paper is to extend the analysis of ruin-related quantities to the delayed renewal risk models. First, the background for the delayed renewal risk model is introduced and a general equation that is used as a framework is derived. The equation is obtained by conditioning on the first drop below the initial surplus level. Then, we consider the deficit at ruin among many random variables associated with ruin. The properties of the distribution function (DF) of the proper deficit are examined in particular.