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Ruin problems under IBNR Dynamics
Applied Stochastic Models in Business and Industry
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.
Discrete-time risk process, Convex order, IBNR claims, Large deviations, Martingale, Ultimate ruin probability
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