Abstract
In this paper, we consider a discrete‐time risk process allowing for delay in claim settlement, which introduces a certain type of dependence in the process. From martingale theory, an expression for the ultimate ruin probability is obtained, and Lundberg‐type inequalities are derived. The impact of delay in claim settlement is then investigated. To this end, a convex order comparison of the aggregate claim amounts is performed with the corresponding non‐delayed risk model, and numerical simulations are carried out with Belgian market data. Copyright © 2011 John Wiley & Sons, Ltd.
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