Modelling Dependencies in Airport Passenger Claim Data Using Copulas

Every year, thousands of passengers flying through U.S. airports file claims to the Transportation Security Administration (TSA). The objective of this dissertation is to use copulas to model dependencies in counts and severities for TSA claims, during the years 2007-2015. Initially, monthly claim counts and amounts are aggregated from daily records, according to their type and site. These monthly series are detrended and fit into different probability distributions using Maximum Likelihood Estimation (MLE), to obtain the corresponding parameters. Once the marginal distributions are obtained, it is possible to fit them into different bivariate copulas. These bivariate copulas are used to determine different tail dependence measures and to highlight non-linear dependencies between the variables. The final procedure involves fitting multivariate copulas and performing simulations. These simulations contrast risk measures like monthly Value at Risk (VaR) and Tail Value at Risk (TVaR) estimates for the different copulas used, along with the independence case and historical values. The results show modelling claims with copulas can yield higher risk measures than the historical values, for random variables with heavy-tailed distributions. The choice of the copula used is also important in this sense, as different copulas generate different simulated risk measures. All of the data processing and modelling is performed using different open source Python libraries.