Miljkovic,TatjanaTatjana Miljkovichttp://hdl.handle.net/2374.MIA/58132024-03-29T05:14:55Z2024-03-29T05:14:55ZModeling Frequency and Severity of Claims with the Zero-Inflated Generalized Cluster-Weighted ModelsPočučaa, NikolaJevtićb, PetarMcNicholasa, PaulMiljkovicc, Tatjanahttp://hdl.handle.net/2374.MIA/68322022-06-24T19:20:02ZModeling Frequency and Severity of Claims with the Zero-Inflated Generalized Cluster-Weighted Models
Počučaa, Nikola; Jevtićb, Petar; McNicholasa, Paul; Miljkovicc, Tatjana
In this paper, we propose two important extensions to cluster-weighted models (CWMs).
First, we extend CWMs to have generalized cluster-weighted models (GCWMs) by allowing
modeling of non-Gaussian distribution of the continuous covariates, as they frequently
occur in insurance practice. Secondly, we introduce a zero-inflated extension
of GCWM (ZI-GCWM) for modeling insurance claims data with excess zeros coming
from heterogenous sources. Additionally, we give two expectation-optimization (EM)
algorithms for parameter estimation given the proposed models. An appropriate simulation
study shows that, for various settings and in contrast to the existing mixture-based
approaches, both extended models perform well. Finally, a real data set based on French
auto-mobile policies is used to illustrate the application of the proposed extensions.
Using Model Averaging to Determine Suitable Risk Measure EstimatesMiljkovic, TatjanaGrun, Bettinahttp://hdl.handle.net/2374.MIA/68312022-06-23T20:39:40ZUsing Model Averaging to Determine Suitable Risk Measure Estimates
Miljkovic, Tatjana; Grun, Bettina
Recent research in loss modeling resulted in a growing number of classes of statistical models as well as additional models being proposed within each class. Empirical results indicate that a range of models within or between model classes perform similarly well, as measured by goodness-of-fit or information criteria, when fitted to the same data set. This leads to model uncertainty and makes model selection a challenging task. This problem is particularly virulent if the resulting risk measures vary greatly between and within the model classes. We propose an approach to estimate risk measures that accounts for model selection uncertainty based on model averaging. We exemplify the application of the approach considering the class of composite models. This application considers 196 different left-truncated composite models previously used in the literature for loss modeling and arrives at point estimates for the risk measures that take model uncertainty into account. A simulation study highlights the benefits of this approach. The data set on Norwegian fire losses is used to illustrate the proposed methodology.
Identifying subgroups of age and cohort effects in obesity prevalenceMiljkovic, TatjanaWang, Xinhttp://hdl.handle.net/2374.MIA/68302022-06-16T21:18:25ZIdentifying subgroups of age and cohort effects in obesity prevalence
Miljkovic, Tatjana; Wang, Xin
The obesity epidemic represents an important public health issue in the United States. Studying obesity trends across age groups over time helps to identify crucial relationships between the disease and medical treatment allowing for the development of effective prevention policies. We aim to define subgroups of age and cohort effects in obesity prevalence over time by considering an optimization approach applied to the age-period-cohort (APC) model. We consider a heterogeneous regression problem where the regression coefficients are age dependent and belong to subgroups with unknown grouping information. Using the APC model, we apply the alternating direction method of multipliers (ADMM) algorithm to develop a two-step algorithm for (1) subgrouping of cohort effects based on similar characteristics and (2) subgrouping age effects over time. The proposed clustering approach is illustrated for the United States population, aged 18–79, during the period 1990–2017.
Assessing the performance of confidence intervals for high quantiles of Burr XII and Inverse Burr mixturesMiljkovica, TatjanaCauseyb, RyanJovanovicc, Milanhttp://hdl.handle.net/2374.MIA/68292022-06-16T21:10:26ZAssessing the performance of confidence intervals for high quantiles of Burr XII and Inverse Burr mixtures
Miljkovica, Tatjana; Causeyb, Ryan; Jovanovicc, Milan
Recent research in the area of univariate mixture modeling indicated that the finite mixture models based on Burr and Inverse Burr component distributions perform well in the modeling of heavy-tail insurance data. Mixture models are able to capture the multimodality which is quite a common characteristic of insurance losses. Through an extensive simulation study, we assess the performance of three different methods in building the confidence intervals for high quantiles of the mixtures of Burr and Inverse Burr distributions. First, we provide mathematical justification for linking the tail of the k-Burr and k-Inverse Burr mixtures to the maximum domain of attraction of the Frechet distribution which allows us to employ the Generalized Pareto Distribution (GPD) in the estimation of high quantiles and their corresponding confidence intervals. Then, we compare these results to those obtained using order statistics and the bootstrap methods. We also modified the existing Peak Over Threshold (POT) algorithm for the efficient computation of the confidence intervals in the upper tail of these mixture models. A real data set on Danish Fire Losses is used to illustrate the application of these methods in practice.