Document ESAIM: P&S, June 2007, Vol. 11, pp. 217-235
DOI: 10.1051/ps:2007016
Discrete Lundberg-type bounds with actuarial applications
Kristina SendovaDepartment of Statistical and Actuarial Sciences, University of Western Ontario, 1151 Richmond St., London, ON, N6A 5B7, Canada; ksendova@stats.uwo.ca
(Received March 6, 2006. Revised August 4, 2006. Published online 19 June 2007.)
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.
Mathematics Subject Classification. 62E99, 60G51, 62P05
Key words: Deficit at ruin, discrete renewal equation, probability of ultimate ruin, stop-loss premium, surplus immediately before ruin.
© EDP Sciences, SMAI 2007