On a partial integrodifferential equation of Seal¿s type

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<title>On a partial integrodifferential equation of Seal¿s type</title>
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<namePart>Willmot, Gordon E.</namePart>
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<abstract displayLabel="Summary">In this paper we generalize a partial integrodifferential equation satisfied by the finite time ruin probability in the classical Poisson risk model. The generalization also includes the bivariate distribution function of the time of and the deficit at ruin. We solve the partial integrodifferential equation by Laplace transforms with the help of Lagrange¿s implicit function theorem. The assumption of mixed Erlang claim sizes is then shown to result in tractable computational formulas for the finite time ruin probability as well as the bivariate distribution function of the time of and the deficit at ruin. A more general partial integrodifferential equation is then briefly considered.</abstract>
<note type="statement of responsibility">Gordon E. Willmot</note>
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<title>Insurance : mathematics and economics</title>
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<publisher>Oxford : Elsevier, 1990-</publisher>
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<identifier type="issn">0167-6687</identifier>
<identifier type="local">MAP20077100574</identifier>
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<text>04/05/2015 Volumen 62 - mayo 2015 </text>
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