MMN-757
Necessary and sufficient condition for the boundedness of the Gerber-Shiu function in dependent Sparre Andersen model
Abstract
In this paper we investigate the boundedness of the Gerber-Shiu expected
discounted penalty function applied in insurance mathematics. We give a
necessary and sufficient condition for its boundedness. This condition is
essentially the boundedness of the conditional expectation given the ruin
occurs at the first claim. It assures that the integral equation satisfied by
the Gerber-Shiu function has a unique bounded solution and it is exactly the
Gerber-Shiu function. By the help of the proven necessary and sufficient
condition we can also simplify the theorem concerning the necessary and
sufficient condition for the limit property. We do not assume independence
between the inter-claim time and the claim size but the results can be applied
to the usually investigated independent case as well. We present examples to
show the applicability of the condition.
Vol. 15 (2014), No. 1, pp. 159-170