Ruin problems under IBNR dynamics

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.

A delayed dual risk model

“…IBNR (Incurred But Not Reported) and IBNR (Reported But Not Settled). A discrete-time model for a risk process allowing claims being delayed was considered in Waters and Papatriandafylou [30] and Trufin et al [29]. Boogaert and Haezendonck [8] studied a liability process with delays in the framework of economical environment.…”

A Risk Model with Delayed Claims

“…Waters and Papatriandafylou (1985) and Trufin et al (2011) considered a discretetime model for a risk process allowing delayed claims. Boogaert and Haezendonck (1989) discussed a liability process with settling delay in the framework of an economic environment.…”

On a Discrete Interaction Risk Model with Delayed Claims

“…In the case of two classes of business, Wu and Yuen [16] consider an interaction risk model with delayed claims and derive a recursive equation for the finite time survival probabilities. More results about risk models with delayed claim settlements can be found in [17][18][19].…”