On Evaluation of the Conditional Distribution of the Deficit at the Time of Ruin

Gordon Willmot

Scandinavian Actuarial Journal, 2000, vol. 2000, issue 1, 63-79

Abstract: 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.

Date: 2000
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DOI: 10.1080/034612300750066737

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