On the generalized gerber. Shiu function for surplus processes with interest

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<title>On the generalized gerber. Shiu function for surplus processes with interest</title>
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<abstract displayLabel="Summary">In this paper, we study the generalized expected discounted penalty (GerberShiu) function in a risk process with credit and debit interests. We define Tu,z to be the first time that the surplus process drops below a certain level z from the initial surplus u(>z). The time of ruin and the time of absolute ruin are special cases of this stopping time. The generalized GerberShiu function is defined on three random variables: the first time that the surplus drops below z from u, Tu,z, the surplus prior to Tu,z, and the amount by which the surplus is below z. An explicit expression for the GerberShiu function when u=z is obtained when the credit and debit interest rates are equal, and explicit results for the GerberShiu function under exponential claims are then obtained. Using these results, we investigate the probability that the surplus reaches an upper level without dropping below a lower level and the distribution of the maximum severity of ruin</abstract>
<note type="statement of responsibility">Shuanming Li</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>
<part>
<text>04/03/2013 Volumen 52 Número 2 - marzo 2013 </text>
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