Casualty Actuarial Society


A Method for Projecting Individual Large Claims

McLennan, Andrew
Murphy, Karl P.

Casualty Actuarial Society Forum Casualty Actuarial Society - Arlington, Virginia
2006: Fall
205 - 236


Motivation: The paper will address the issue of estimating the uncertainty in the run off of individual large claims in insurance portfolios, which is often the primary source of uncertainty in the reserving risk component of insurance risk.

Method: The paper begins by reviewing current methodologies for estimating the uncertainty in loss reserves. Methods until now have focused on aggregate modeling of gross or net of reinsurance loss reserves, and no direct connection between the distribution of gross and net reserves. The paper develops a non-parametric framework to simulate the distribution of ultimate position of large claims, both reported and large IBNR claims. The method samples the development of individual claims based on the historic development of large claims, incorporating information at an aggregate level surrounding reserving strength. The model also predicts when claims will settle, and the timing of claim payments.

Results: The method developed is not intended to replace existing aggregate modeling, but is an improvement to traditional methods which estimate the variability of gross of reinsurance loss reserves, and is a useful tool to allow for reinsurance recoveries more accurately. By individually projecting the ultimate position of large claims, we can explicitly allow for policy or contract limits. Further, we can apply any reinsurance program structure to the gross results, including allowance for aggregate deductibles, incomplete placements, retrocessions to captive reinsurers, indexation clues, and different treaty attachment rules (ie Losses Occurring During vs Risks Attaching). The paper then shows how the variability of attritional claims can be estimated using traditional stochastic methods, and the attritional claims can be estimated using traditional stochastic methods, and the attritional and large results can be combined to estimate the variability of the aggregate portfolio of loss reserves.

Keywords: Reserving, Large Claims, Reinsurance, Stochaistic Modeling, Simulation, Capital Modeling, IBNR.

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