Miljkovic,Tatjana
miljkot
Recent Submissions
Item Modeling Frequency and Severity of Claims with the Zero-Inflated Generalized Cluster-Weighted Models
Počučaa, Nikola; Jevtićb, Petar; McNicholasa, Paul; Miljkovicc, TatjanaIn 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.Item Using Model Averaging to Determine Suitable Risk Measure Estimates
Miljkovic, Tatjana; Grun, BettinaRecent 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.Item Identifying subgroups of age and cohort effects in obesity prevalence
Miljkovic, Tatjana; Wang, XinThe 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.Item Assessing the performance of confidence intervals for high quantiles of Burr XII and Inverse Burr mixtures
Miljkovica, Tatjana; Causeyb, Ryan; Jovanovicc, MilanRecent 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.Item Mixture modeling of data with multiple partial right-censoring levels
Semhar, Michael; Miljkovic, Tatjana; Melnykov, VolodymyrIn this paper, a new flexible approach to modeling data with multiple partial right-censoring points is proposed. This method is based on finite mixture models, flexible tool to model heterogeneity in data. A general framework to accommodate partial censoring is considered. In this setting, it is assumed that a certain portion of data points are censored and the rest are not. This situation occurs in many insurance loss data sets. A novel probability function is proposed to be used as a mixture component and the expectation-maximization algorithm is employed for estimating model parameters. The Bayesian information criterion is used for model selection. Additionally, an approach for the variability assessment of parameter estimates as well as the computation of quantiles commonly known as risk measures is considered. The proposed model is evaluated using a simulation study based on four common probability distribution functions used to model right skewed loss data and applied to a real data set with good results.Item An exploration of gender gap using advanced data science tools: actuarial research community
Yu, Mengyu; Krehbiel, Mazie; Thompson, Samantha; Miljkovic, TatjanaThis paper explores the role of gender gap in the actuarial research community with advanced data science tools. The web scraping tools were employed to create a database of publications that encompasses six major actuarial journals. This database includes the article names, authors’ names, publication year, volume, and the number of citations for the time period 2005–2018. The advanced tools built as part of the R software were used to perform gender classification based on the author’s name. Further, we developed a social network analysis by gender in order to analyze the collaborative structure and other forms of interaction within the actuarial research community. A Poisson mixture model was used to identify major clusters with respect to the frequency of citations by gender across the six journals. The analysis showed that women’s publishing and citation networks are more isolated and have fewer ties than male networks. The paper contributes to the broader literature on the “Matthew effect” in academia. We hope that our study will improve understanding of the gender gap within the actuarial research community and initiate a discussion that will lead to developing strategies for a more diverse, inclusive, and equitable community.Item A new computational approach for estimation of the Gini index based on grouped data
Miljkovic, Tatjana; Chen, Ying-JuMany government agencies still rely on the grouped data as the main source of infor- mation for calculation of the Gini index. Previous research showed that the Gini index based on the grouped data suffers the first and second- order correction bias compared to the Gini index computed based on the individual data. Since the accuracy of the estimated correction bias is subject to many underlying assumptions, we propose a new method and name it D-Gini, which reduces the bias in Gini coefficient based on grouped data. We investigate the performance of the D-Gini method on an open-ended tail interval of the income distribution. The results of our simulation study showed that our method is very effective in minimizing the first and second order-bias in the Gini index and outperforms other methods previously used for the bias-correction of the Gini index based on grouped data. Three data sets are used to illustrate the application of this method.Item Extending Composite Loss Models Using a General Framework of Advanced Computational Tools
Grun, Bettina; Miljkovic, TatjanaComposite models have a long history in actuarial science because they provide a flexible method of curve-fitting for heavy-tailed insurance losses. The ongoing research in this area continuously suggests methodological improvements for existing composite models and considers new composite models. A number of different composite models have been previously proposed in the literature to fit the popular data set related to Danish fire losses. This paper provides the most comprehensive analysis of composite loss models on the Danish fire losses data set to date by evaluating 256 composite models derived from 16 parametric distributions that are commonly used in actuarial science. If not suitably addressed, inevitable computational challenges are encountered when estimating these composite models that may lead to suboptimal solutions. General implementation strategies are developed for parameter estimation in order to arrive at an automatic way to reach a viable solution, regardless of the specific head and/or tail distributions specified. The results lead to an identification of new well-fitting composite models and provide valuable insights into the selection of certain composite models for which the tail-evaluation measures can be useful in making risk management decisions.Item Modeling Impact of Natural Hazard- Induced Disasters on Income Distribution in the United States
Fang, Lin; Wu, Jiayu; Miljkovic, TatjanaEconomic damage due to hurricane activities has been shown to impact income inequality in the coastal states of the United States. We consider 17 other natural hazards, in addition to hurricanes, that affected the entire United States for the period 1970–2013. Two fixed effects models were developed to quantify the relationship between income inequality and economic and demographic variables, including crop and property losses from natural hazard-induced disasters. These models include state-byyear and region-by-year fixed effects models. Our findings show that the damages from all natural hazards impact income distribution across the United States, not only in hurricane-affected areas, but also in non-hurricane states. The results of our study have important implications for the insurance industry and government policymakers.Item A new analysis of VIX using mixture of regressions: Examination and short-term forecasting for the S & P 500 market
Miljkovic, Tatjana; SenGupta, IndranilA novel approach to the analysis of S & P 500 market fluctuations is proposed using a K‐component mixture of regressions model. The Barndorff‐Nielsen and Shephard stochastic model is employed where the estimates of jumps of log‐returns are governed by Lévy subordinators. Daily VIX and VIX2 close prices are analyzed as the indicators of log‐return volatility and the corresponding variance of the S & P 500 index using the mixture model. The behavior of the S & P 500 market from 1 August 2005 to 31 December 2009 is analyzed and forecasted. A set of rules are provided to predict monthly fluctuation in the S & P 500 market. The procedure used in this paper gives a novel approach for constructing an “indicator”of non‐Gaussian jump of an empirical data set in finance using mixture of regression (Gaussian) analysis.Item On Two Mixture-Based Clustering Approaches Used in Modeling an Insurance Portfolio
Miljkovic, Tatjana; Fernández, DanielWe review two complementary mixture-based clustering approaches for modeling unobserved heterogeneity in an insurance portfolio: the generalized linear mixed cluster-weighted model (CWM) and mixture-based clustering for an ordered stereotype model (OSM). The latter is for modeling of ordinal variables, and the former is for modeling losses as a function of mixed-type of covariates. The article extends the idea of mixture modeling to a multivariate classification for the purpose of testing unobserved heterogeneity in an insurance portfolio. The application of both methods is illustrated on a well-known French automobile portfolio, in which the model fitting is performed using the expectation-maximization (EM) algorithm. Our findings show that these mixture-based clustering methods can be used to further test unobserved heterogeneity in an insurance portfolio and as such may be considered in insurance pricing, underwriting, and risk management.Item Examining the Impact on Mortality Arising from Climate Change: Important Findings for the Insurance Industry
Miljkovic, Tatjana; Miljkovic, Dragan; Maurer, KarstenIn this paper, we analyze the impact on overall mortality rates for the general US population arising from climate change and the weather events resulting in property damages for the period 1968–2013. We develop a fixed effects panel data model for the impact of climate change on property damage, with precipitation having a more pronounced effect than extreme temperatures. Using the Dumitrescu–Hurlin panel data causality test, we found that property damages Granger cause an increase in mortality rates for the middle age and old age population. Therefore, property damage can further be used to improve the prediction of future mortality rates in the US. Our findings are important for the insurance industry, which is currently seeking ways to incorporate the impact of climate change. The industry is developing the Actuaries Climate Index and the Actuaries Climate Risk Index which have the objective of informing the insurance industry about the impact of extreme weather and its associated risks.Item Ratemaking for a New Territory: Enhancing GLM Pricing Model with a Bayesian Analysis
Zhang, Jing; Miljkovic, TatjanaItem An evaluation of the reconstructed coefficient of determination and potential adjustments
Miljkovic, Tatjana; Orr, MeganPreviously, a method was proposed for calculating a reconstructed coefficient of determination in the case of right-censored regression using the expectation–maximization (EM) algorithm. This measure is assessed via simulation study for the purpose of evaluating the utility of model fit. Further, several reconstructed adjusted coefficients of determination are proposed and compared via simulation study for the purpose of model selection. The application of these proposed measures is illustrated on a real dataset.Item Fouling-Release Performance of Silicone Oil-Modified SiloxanePolyurethane Coatings
Galhenage, Teluka P.; hoffman, Dylan; Silbert, Samantha D.; Stafslien, Shane J.; Daniels, Justin; Miljkovic, Tatjana; Finlay, John A.; Franco, Sofia C.; Clare, Anthony S.; Nedved, Brian T.; Hadfield, Michael G.; Wendt, Dean E.; Waltz, Grant; Brewer, Lenora; Teo, Serena L.M.; Lim, Chin-Sing; Webster, Dean C.The effect of incorporation of silicone oils into a siloxanepolyurethane fouling-release coatings system was explored. Incorporation of phenylmethyl silicone oil has been shown to improve the fouling-release performance of silicone-based fouling-release coatings through increased interfacial slippage. The extent of improvement is highly dependent upon the type and composition of silicone oil used. The siloxane-polyurethane (SiPU) coating system is a tough fouling-release solution, which combines the mechanical durability of polyurethane while maintaining comparable fouling-release performance with regard to commercial standards. To further improve the fouling-release performance of the siloxane-PU coating system, the use of phenylmethyl silicones oils was studied. Coatings formulations were prepared incorporating phenylmethyl silicone oils having a range of compositions and viscosities. Contact angle and surface energy measurements were conducted to evaluate the surface wettability of the coatings. X-ray photoelectron spectroscopy (XPS) depth profiling experiments demonstrated self-stratification of silicone oil along with siloxane to the coating-air interface. Several coating formulations displayed improved or comparable fouling-release performance to commercial standards during laboratory biological assay tests for microalgae (Navicula incerta), macroalgae (Ulva linza), adult barnacles (Balanus amphitrite syn. Amphibalanus amphitrite), and mussels (Geukensia demissa). Selected silicone-oilmodified siloxane-PU coatings also demonstrated comparable fouling-release performance in field immersion trials. In general, modifying the siloxane-PU fouling-release coatings with a small amount (1−5 wt % basis) of phenylmethyl silicone oil resulted in improved performance in several laboratory biological assays and in long-term field immersion assessments.Item Modeling loss data using mixtures of distributions
Miljkovic, Tatjana; Grün, BettinaIn this paper, we propose an alternative approach for flexible modeling of heavy tailed, skewed insurance loss data exhibiting multimodality, such as the well-known data set on Danish Fire losses. Our approach is based on finite mixture models of univariate distributions where all K components of the mixture are assumed to be from the same parametric family. Six models are developed with components from parametric,on-Gaussian families of distributions previously used in actuarial modeling: Burr, Gamma, Inverse Burr, Inverse Gaussian, Log-normal, and Weibull. Some of these component distributions are already alone suitable to model data with heavy tails, but do not cover the case of multimodality. Estimation of the models with a fixed number of components K is proposed based on the EM algorithm using three different initialization strategies: distance-based, k-means, and random initialization. Model selection is possible using information criteria, and the fitted models can be used to estimate risk measures for the data, such as VaR and TVaR. The results of the mixture models are compared to the composite Weibull models considered in recent literature as the best models for modeling Danish Fire insurance losses. The results of this paper provide new valuable tools in the area of insurance loss modeling and risk evaluation.Item Redefining standards for body mass index of the US population based on BRFSS data using mixtures
Miljkovic, Tatjana; Shaik, Saleem; Miljkovic, DraganUsing body mass index (BMI) data from 2012 Behavioral Risk Factor Surveillance System, we test a spectrum of single parametric skewed distributions as well as Gaussian mixture densities to determine best distributional fit. We find that a k-component Gaussian mixture is the best model to describe the distribution of BMI data for the overall US population and for the population divided by gender, race, and region. A 4-component Gaussian mixture with the following subpopulation means (standard deviations) fits best the US population: 22.21(σ = 2.27), 26.05(σ = 2.19), 29.83(σ = 3.90), 35.47(σ = 8.45) with corresponding weights: 23%, 25%, 37%, and 15%. Current obesity standards are set based on a convention and they are fairly dated. Overweight population has BMI (25.0, 29.9). Obese population is subdivided into three grades based on BMI: grade 1 (30–35), grade 2 (35–40), grade 3 (40 and above). Our study shows that modeling BMI using mixtures can be used to redefine current standards and support them with actual prevalence rather than a dated convention. By redefining BMI standards and employing the mixture models by gender and race, health and food policy makers will have opportunity to diversify policies and treatments of obesity as premier public health problem in the USA.Item UTILIZATION OF MODIFIED WHEAT AND TAPIOCA STARCHES AS FAT REPLACEMENTS IN BREAD FORMULATION
Balic, Ratko; Miljkovic, Tatjana; Ozsisli, Bahri; Simsek, SenayUsing fat in bread production is expensive, and from the diet point of view, it counts as high caloric food. Since obesity is a significant problem in the USA and many other countries, food industries are turning to the fat replacers in food. This research investigated the effectiveness of octenyl succinate anhydride (OSA) modified starches, from two sources (wheat and tapioca), as fat replacers in bread formulation. Sample for control was 2% shortening, and for test samples 2% and 4% OSA modified starch and tapioca were used as fat replacers. Tests were performed on dough and baked product (bread). Results showed that samples with 4% OSA modified wheat and tapioca starch can be used as fat replacers in bread production. Dough and bread properties in comparison with control sample with 2% shortening had better or the same characteristics.Item Modeling veterans’ health benefit grants using the expectation maximization algorithm
Miljkovic, Tatjana; Barabanov, NikitaA novel application of the expectation maximization (EM) algorithm is proposed for modeling rightcensored multiple regression. Parameter estimates, variability assessment, and model selection are summarized in a multiple regression settings assuming a normal model. The performance of this method is assessed through a simulation study. New formulas for measuring model utility and diagnostics are derived based on the EM algorithm. They include reconstructed coefficient of determination and influence diagnostics based on a one-step deletion method. A real data set, provided by North Dakota Department of Veterans Affairs, is modeled using the proposed methodology. Empirical findings should be of benefit to government policy-makers.