G. Willmot, E., On Evaluation of the Conditional Distribution of the Deficit at the Time of Ruin, Scandinavian actuarial journal , 2000(1), 2000, pp. 63-79
Analytic evaluation of the deficit at the time of ruin is shown to be simplified when the residual equilibrium density function associated with the claim size distribution has a certain property. This result is used to show that the conditional distribution of the deficit is a mixture of Erlangs (gamma with integer shape parameters) if the same is true of the claim size distribution. This unifies and generalizes previous results involving combinations of exponentials and a particular Erlang distribution. Extensions are then discussed.