On Evaluation of the Conditional Distribution of the Deficit at the Time of Ruin |
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Authors: | Gordon E Willmot |
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Institution: | Department of Mathematics , ETH Zurich , CH-8092, Zurich, Switzerland |
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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. |
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Keywords: | Combinations Exponentials Duration Negati Surplus Mixture Erlangs Residual Equilibrium Distribution |
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