Discrete Lundberg-type bounds with actuarial applications
ESAIM: Probability and Statistics, Tome 11 (2007), pp. 217-235.

Different kinds of renewal equations repeatedly arise in connection with renewal risk models and variations. It is often appropriate to utilize bounds instead of the general solution to the renewal equation due to the inherent complexity. For this reason, as a first approach to construction of bounds we employ a general Lundberg-type methodology. Second, we focus specifically on exponential bounds which have the advantageous feature of being closely connected to the asymptotic behavior (for large values of the argument) of the renewal function. Finally, the last section of this paper includes several applications to risk theory quantities.

DOI : 10.1051/ps:2007016
Classification : 62E99, 60G51, 62P05
Mots-clés : deficit at ruin, discrete renewal equation, probability of ultimate ruin, stop-loss premium, surplus immediately before ruin 
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     author = {Sendova, Kristina},
     title = {Discrete {Lundberg-type} bounds with actuarial applications},
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     mrnumber = {2320817},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ps:2007016/}
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Sendova, Kristina. Discrete Lundberg-type bounds with actuarial applications. ESAIM: Probability and Statistics, Tome 11 (2007), pp. 217-235. doi : 10.1051/ps:2007016. http://archive.numdam.org/articles/10.1051/ps:2007016/

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