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Aggregate Excess-of-Loss Under Extreme Risk, A Reinsurance Model with Frechet Claims
AuthorLuerken, Erick Lothar
AdvisorAlparslan, Ugur T
Mathematics and Statistics
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Insurance companies make a profit by assuming another party's risk in return for incremental payments. While most routine losses won't force the insurance company into bankruptcy, sometimes, ccertain extreme events, such as Hurricane Katrina, occur which create losses so great that it would ruin the insurance company. In order to prevent this from occurring, many insurance companies purchase reinsurance to manage their risk. However, in order to maximize their profits, they would like to spend as little as they can on this protection. To help estimate the amount of loss that an insurance company should expect to face in a deterministic time interval, we have developed a method that estimates the total summed excess of claims above a threshold. In our research, we have fitted claims to three heavy tailed distributions, Pareto, Loggamma, and $\alpha$-stable in order to account for extreme losses. For various values of $\alpha \in (1,2)$, we ran several thousand loops, with each loop simulated over a million claims. Next, the net exceedance was computed for each loop and compared to our theoretical mean exceedance. Our results showed that this method was more accurate for values of $\alpha$ close to 2 and lower thresholds. Pareto claims more closely matched the theoretical estimate than the other two claims, followed by $\alpha$-stable and Loggamma.