Our general research area is focused on determining the two-sided interval estimators for risk measures in modeling loss data. In this case, we are looking at the conditional tail expectation (CTE) for Pareto tails (specifically Pareto I and Pareto II). We use the Delta Method to compute the confidence intervals, and compare the performance with Bootstrapping. Our work was conducted by researching other papers on conditional tail expectations, and using these as a guide to perform the same computations with the Pareto distributions. We computed the VaR, CTE, Hessian matrix, and corresponding gradient vectors by hand in order to find the interval estimations for risk measures. We perform simulations in R to compute the Delta Method and Bootstrapping confidence intervals at levels p=0.95 and p=0.99. We then graph these results to compare the performance of the two methods. Our primary research question is to explore techniques not used before to estimate the CTE for families of the Pareto distribution. Within actuarial science, these techniques are used to help better understand loss data.The major finding is an alternative technique to estimate the variance of the Pareto tails. We discovered the Delta Method produces smaller confidence intervals for CTE compared to Bootstrapping. As we move forward, we hope to develop this method for more complex children of the Feller-Pareto distribution. As a student going into the Actuarial Science field, Pareto distributions are often used when looking at the loss models for certain insurance losses. This will be helpful in determining whether an insurance product will be profitable in the event of a catastrophe of the top tail of losses.
Author(s): Justus Thomas, Data Science and Statistics Major
Hannah Waler, Data Science and Statistics Major
Advisor(s): Tatjana Miljkovic, Department of Statistics
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