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Discrete Lundberg-type bounds with actuarial applications

Published online by Cambridge University Press:  19 June 2007

Kristina Sendova
Kristina Sendova*
Affiliation:
Department of Statistical and Actuarial Sciences, University of Western Ontario, 1151 Richmond St., London, ON, N6A 5B7, Canada; ksendova@stats.uwo.ca
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Abstract

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.

Keywords

Deficit at ruindiscrete renewal equationprobability of ultimate ruinstop-loss premiumsurplus immediately before ruin.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 217 - 235
Copyright
© EDP Sciences, SMAI, 2007

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