Frequency Of Claims Research Articles

A comparative analysis of several multivariate zero-inflated and zero-modified models with applications in insurance

. Given that insurance companies often operate across multiple lines of insurance business, where claim frequencies on different lines are often correlated, it often becomes advantageous to employ multivariate count modeling where dependence between lines of business can be included in the modeling. Due to the operation of bonus-malus systems where there is a reward to the insurance policyholder for not claiming, claims data in automobile insurance often exhibits an excess of common zeros, a characteristic known as multivariate zero-inflation. In this article, we propose two approaches to address this feature. The first approach involves utilizing a multivariate zero-inflated model, where we artificially enhance the probability of common zeros based on standard multivariate count distributions. The second approach applies a multivariate zero-modified model, which separately handles the common zeros and the number of claims incurred in each line given that at least one claim occurs. We present several models under these frameworks, along with detailed inference procedures. In the applications section, we conduct a comprehensive comparative analysis of these models using data from an automobile insurance portfolio.

Enhanced gradient boosting for zero-inflated insurance claims and comparative analysis of CatBoost, XGBoost, and LightGBM

The property and casualty (P&C) insurance industry faces challenges in developing claim predictive models due to the highly right-skewed distribution of positive claims with excess zeros. To address this, actuarial science researchers have employed ‘zero-inflated’ models that combine a traditional count model and a binary model. This paper investigates the use of boosting algorithms to process insurance claim data, including zero-inflated telematics data, to construct claim frequency models. Three popular gradient boosting libraries - XGBoost, LightGBM, and CatBoost -- are evaluated and compared to determine the most suitable library for training insurance claim data and fitting actuarial frequency models. Through a comprehensive analysis of two distinct datasets, it is determined that CatBoost is the best for developing auto claim frequency models based on predictive performance. Furthermore, we propose a new zero-inflated Poisson boosted tree model, with variation in the assumption about the relationship between inflation probability p and distribution mean μ, and find that it outperforms others depending on the characteristics of the data. This model enables us to take advantage of particular CatBoost tools, which makes it easier and more convenient to investigate the effects and interactions of various risk features on the frequency model when using telematics data.

A discrete claims-model for the inflated and over-dispersed automobile claims frequencies data: Applications and actuarial risk analysis

A discrete claims-model for the inflated and over-dispersed automobile claims frequencies data: Applications and actuarial risk analysis

A data science approach to climate change risk assessment applied to pluvial flood occurrences for the United States and Canada

Abstract There is mounting pressure on (re)insurers to quantify the impacts of climate change, notably on the frequency and severity of claims due to weather events such as flooding. This is however a very challenging task for (re)insurers as it requires modeling at the scale of a portfolio and at a high enough spatial resolution to incorporate local climate change effects. In this paper, we introduce a data science approach to climate change risk assessment of pluvial flooding for insurance portfolios over Canada and the United States (US). The underlying flood occurrence model quantifies the financial impacts of short-term (12–48 h) precipitation dynamics over the present (2010–2030) and future climate (2040–2060) by leveraging statistical/machine learning and regional climate models. The flood occurrence model is designed for applications that do not require street-level precision as is often the case for scenario and trend analyses. It is applied at the full scale of Canada and the US over 10–25 km grids. Our analyses show that climate change and urbanization will typically increase losses over Canada and the US, while impacts are strongly heterogeneous from one state or province to another, or even within a territory. Portfolio applications highlight the importance for a (re)insurer to differentiate between future changes in hazard and exposure, as the latter may magnify or attenuate the impacts of climate change on losses.

The usage and costs of national drug price-negotiated anticancer medicines in a first-tier city in Northeast China: a study based on health insurance data

BackgroundThe National Drug Price Negotiation (NDPN) policy has entered a normalisation stage, aiming to alleviate, to some extent, the disease-related and economic burdens experienced by cancer patients. This study analysed the use and subsequent burden of anticancer medicines among cancer patients in a first-tier city in northeast China.MethodsWe assessed the usage of 64 negotiated anticancer medicines using the data on the actual drug deployment situation, the frequency of medical insurance claims and actual medication costs. The affordability of these medicines was measured using the catastrophic health expenditure (CHE) incidence and intensity of occurrence. Finally, we used the defined daily doses (DDDs) and defined daily doses cost (DDDc) as indicators to evaluate the actual use of these medicines in the region.ResultsDuring the study period, 63 of the 64 medicines were readily available. From the perspective of drug usage, the frequency of medical insurance claims for negotiated anticancer medicines and medication costs showed an increasing trend from 2018 to 2021. Cancer patients typically sought medical treatment at tertiary hospitals and purchased medicines at community pharmacies. The overall quantity and cost of medications for patients covered by the Urban Employee Basic Medical Insurance (UEBMI) were five times higher than those covered by the Urban and Rural Resident Medical Insurance (URRMI). The frequency of medical insurance claims and medication costs were highest for lung and breast cancer patients. Furthermore, from 2018 to 2021, CHE incidence showed a decreasing trend (2.85–1.60%) under urban patients’ payment capability level, but an increasing trend (11.94%–18.42) under rural patients’ payment capability level. The average occurrence intensities for urban (0.55–1.26 times) and rural (1.27–1.74 times) patients showed an increasing trend. From the perspective of drug utilisation, the overall DDD of negotiated anticancer medicines showed an increasing trend, while the DDDc exhibited a decreasing trend.ConclusionThis study demonstrates that access to drugs for urban cancer patients has improved. However, patients’ medical behaviours are affected by some factors such as hospital level and type of medical insurance. In the future, the Chinese Department of Health Insurance Management should further improve its work in promoting the fairness of medical resource distribution and strengthen its supervision of the nation’s health insurance funds.

Determination of Insurance Premium Rates with Aggregation Claims at BPJS with Exponential and Gamma Distributions

Badan Penyelenggara Jaminan Sosial (BPJS) is a legal entity that has been provided by the government for the community with the aim of providing protection for all workers in Indonesia from certain socio-economic risks. National development, marked by planned and continuous strides, embodies a commitment to engage all societal, national, and state levels in fostering progress. Encompassing political, economic, socio-cultural, and defense and security realms, the development is meticulously designed to be comprehensive, targeted, integrated, gradual, and sustainable. The overarching objective is to catalyze an augmentation of national capabilities, align the standard of living for the Indonesian people with developed nations, and elevate overall welfare. To establish premium rates, a method involves multiplying the conditional expected value of claim frequency by the size of the claim, considering observed risk characteristics. A claim, in this context, constitutes a formal request to the insurance company, seeking payment in accordance with the terms of the agreement. The primary objective of this study is to establish the insurance premium rates applicable to policyholders (the insured) through the estimation of parameters in the distribution governing aggregate claims. This involves the distribution of both the number of claims and the size of the claims, and the estimation is performed using the moment method. Premium computations are executed based on two key principles: the pure premium principle and the expected value principle. This research produces the conclusion that the Poisson-Gamma aggregate claims distribution has a premium amount of 3.61 times greater than Poisson-Exponential due to the application of the anticipated value principle, namely IDR 4,403,542.94 per month and IDR 1,219,878.45 per month, respectively.

Mining Injuries 2012-2019: Using Workers' Compensation Claims Data From 35 States to Identify Rates and Costs Associated by Nature of Injury, Event/Exposure, and Body Part Affected.

This study summarized the frequency and cost of mining-related injuries. Mining-related workers' compensation (WC) claims data from 35 states were summarized to report counts, claim rates, and costs for 2012-2019. These data were compared with Mine Safety and Health Administration injury and employment data for the same period. Despite system differences, both WC and Mine Safety and Health Administration counts and rates declined over time and injury patterns were similar. Total WC costs were approximately $2.325B. Medical-only claims represented 59.4% of the claims by count, but only 3.3% of costs. Lost-time nonfatal claims represented 40.2% of the claims by count, but 90.2% of costs. Claims frequency and costs varied greatly by injury event/exposure, part of body, and nature. Injury frequency has declined but costs remain high. The most costly and disabling cases were identified.

Combined modelling of micro-level outstanding claim counts and individual claim frequencies in non-life insurance

Usually, the actuarial problems of predicting the number of claims incurred but not reported (IBNR) and of modelling claim frequencies are treated successively by insurance companies. New micro-level methods designed for large datasets are proposed that address the two problems simultaneously. The methods are based on an elaborated occurrence process model that includes both a claim intensity model and a claim development model. The influence of claim feature variables is modelled by suitable neural networks. Extensive simulation experiments and a case study on a large real data set from a motor legal insurance portfolio show accurate predictions at both the aggregate and individual policy level, as well as appropriate fitted models for claim frequencies. Moreover, a novel alternative approach combining data from classic triangle-based methods with a micro-level intensity model is introduced and compared to the full micro-level approach.

A representation-learning approach for insurance pricing with images

AbstractUnstructured data are a promising new source of information that insurance companies may use to understand their risk portfolio better and improve the customer experience. However, these novel data sources are difficult to incorporate into existing ratemaking frameworks due to the size and format of the unstructured data. This paper proposes a framework to use street view imagery within a generalized linear model. To do so, we use representation learning to extract an embedding vector containing useful information from the image. This embedding is dense and low dimensional, making it appropriate to use within existing ratemaking models. We find that there is useful information included in street view imagery to predict the frequency of claims for certain types of perils. This model can be used as in a ratemaking framework but also opens the door to future empirical research on attempting to extract which characteristics within the image leads to increased or decreased predicted claim frequencies. Throughout, we discuss the practical difficulties (technical and social) of using this type of data for insurance pricing.

Dietary Counseling Documentation Among Patients Recently Hospitalized for Cardiovascular Disease

BackgroundDiet intervention forms the cornerstone for cardiovascular disease (CVD) management. ObjectiveThe objective was to measure the frequency of dietary counseling documentation for patients recently hospitalized with CVD. DesignThis was an observational study. Participants and settingPatients were included from the Michigan Value Collaborative Multipayer Claims Registry from October 2015 to February 2020. Main outcome measureThe study measured the frequency of medical claims that document dietary counseling ≤90 days after hospitalization (ie, an episode of care) for CVD events (coronary artery bypass grafting, acute myocardial infarction, congestive heart failure, and percutaneous coronary intervention). Dietary counseling documentation was defined as having an encounter-level International Classification of Diseases 10th Revision code for dietary counseling or current procedural terminology code for medical nutrition therapy or cardiac rehabilitation. Statistical analyses performedMultivariable logistic regression was used to measure variation in documentation across gender, age, comorbidities, hospital geography, CVD event, and insurer. ResultsThere were 175,631 episodes of care (congesitve heart failure 47.1%, acute myocardial infarction 28.7%, percutaneous coronary intervention 17.0%, and coronary artery bypass grafting 7.3%) among 146,185 individuals. Most episodes occurred among men (55.8%) and those older than age 65 years (71.9%). Dietary counseling was documented for 22.8% of episodes and was more common as cardiac rehabilitation (18.6%) than other encounter types (5.1%). In multivariable analysis, there was lower odds for dietary counseling documentation among those older than age 65 years (odds ratio [OR] 0.77; P < .001), women (OR 0.83; P < .001), with chronic kidney disease (OR 0.74; P < .001), or diabetes (OR 0.95; P < .001), but greater odds for those with obesity (OR 1.28; P < .001) and nonmetropolitan hospitals (OR 1.31; P < .001). Compared with coronary artery bypass grafting, acute myocardial infarction (OR 0.29; P < .001), confestive heart failure (OR 0.12; P < .001), and percutaneous coronary intervention (OR 0.36; P < .001) episodes had lower odds to have dietary counseling coded. Compared with Traditional Medicare, Medicaid and Medicare Advantage health maintenance organization plans had lower odds, whereas Commercial or Medicare Advantage preferred provider organization and Commercial health maintenance organization plans had higher odds to have dietary counseling documented. Results were mostly similar when evaluated by race. ConclusionsDietary counseling was infrequently documented after hospitalization for CVD episodes in medical claims in a Michigan-based multipayer claims database with large variation by reason for hospitalization and patient factors.

A hospital-based descriptive study of Ayushman Bharat-Pradhan Mantri Jan-Arogya Yojana: an analysis of 4844 claims

Background: Current study was undertaken to analyze Ayushman Bharat claims settled during the initial two years of launch of the scheme in an empaneled, public hospital in northern India. Objective was descriptive analysis of 4844 settled claims in terms of demographic characteristics of beneficiaries, procedures and packages availed by them in an empaneled public hospital during the initial two years of the launch of the scheme. Methods: A cross-sectional records study of 4844 settled claims was conducted in a public, empanelled 1015 bedded tertiary care multi-specialty hospital of north India. Anonymized data was collected from the transaction management module of AB-PMJAY scheme and hospitalization record of patients retrieved from medical records department. Results: The study revealed that around 4844 claims were settled during the initial two years (December 2018 to December 2020). Highest number of claims (43.33%) were availed under general medicine category. Chemotherapy packages availed under medical oncology were 37.45% of all claims. Interventional cardiology packages were the costliest. Conclusions: The study provides an insight into the frequency of various claims, their costs, disease/procedural burden of beneficiary patients of AB-PMJAY. It will provide policy feedback and help in future planning and implementation of the scheme.

Age, Cars, and Claims: Decoding the Insurance Landscape

Embark on a journey through the realms of car insurance modeling, where the fusion of statistical and mathematical prowess unveils the secrets behind predicting claim frequency, severity, and overall costs. This enchanted exploration not only guides you through the wizardry of Python but also empowers you with the art of crafting insurance products, navigating risk, and orchestrating business strategies. If the arcane world of Car Insurance Modeling beckons you, join this mystical narrative, where algorithms and Python spells converge, weaving a tale of predictive mastery. Illuminate your path and delve into the enchantment of modeling automotive destinies with code as your guide

Modeling claims frequency in the Algerian automobile insurance market using machine learning

The Algerian automobile insurance market faces significant challenges in pricing insurance policies due to the lack of reliable predictions for insurance losses. In this paper, we introduce a new ratemaking system that leverages advanced data analysis techniques, including Generalized Linear Models and machine learning algorithms like Neural Networks, boosting, and stacking algorithms, to model claims frequency. By analyzing data and statistics of drivers in the Algerian market, this system offers a data-driven solution that helps insurers to better understand their risk exposure and make informed pricing decisions. The proposed system has implications for both insurers and policyholders in terms of fairer and more accurate pricing, which will ultimately benefit the Algerian economy.&#x0D;

On clustering levels of a hierarchical categorical risk factor

Abstract Handling nominal covariates with a large number of categories is challenging for both statistical and machine learning techniques. This problem is further exacerbated when the nominal variable has a hierarchical structure. We commonly rely on methods such as the random effects approach to incorporate these covariates in a predictive model. Nonetheless, in certain situations, even the random effects approach may encounter estimation problems. We propose the data-driven Partitioning Hierarchical Risk-factors Adaptive Top-down algorithm to reduce the hierarchically structured risk factor to its essence, by grouping similar categories at each level of the hierarchy. We work top-down and engineer several features to characterize the profile of the categories at a specific level in the hierarchy. In our workers’ compensation case study, we characterize the risk profile of an industry via its observed damage rates and claim frequencies. In addition, we use embeddings to encode the textual description of the economic activity of the insured company. These features are then used as input in a clustering algorithm to group similar categories. Our method substantially reduces the number of categories and results in a grouping that is generalizable to out-of-sample data. Moreover, we obtain a better differentiation between high-risk and low-risk companies.

Measuring Discrete Risks on Infinite Domains: Theoretical Foundations, Conditional Five Number Summaries, and Data Analyses

To accommodate numerous practical scenarios, in this article we extend statistical inference for smoothed quantile estimators from finite domains to infinite domains. We accomplish the task with the help of a newly designed truncation methodology for discrete loss distributions with infinite domains. A simulation study illustrates the methodology in the case of several distributions, such as Poisson, negative binomial, and their zero-inflated versions, which are commonly used in the insurance industry to model claim frequencies. Additionally, we propose a very flexible bootstrap-based approach for use in practice. Using automobile accident data and their modifications, we compute what we have termed the conditional five number summary (C5NS) for the tail risk and construct confidence intervals for each of the five quantiles making up C5NS and then calculate the tail probabilities. The results show that the smoothed quantile approach classifies the tail riskiness of portfolios not only more accurately but also produces lower coefficients of variation in the estimation of tail probabilities than those obtained using the linear interpolation approach.

Penentuan Rate Asuransi Kendaraan Bermotor Menggunakan Kredibilitas Bayesian

&lt;p&gt;This paper uses Credibility to determine new rate based on data of historical claim in a motor vehicle insurance in Bandung, Indonesia. Rate is formed based on past loss through experience rating. Credibility is one of the examples of experience rating that considers group historical claims. One of the credibility methods is Bayesian credibility that considers rate as a random variable. Bayesian credibility is used based on claim frequency and claim severity from a group of policy holders in order to create new rates. In this paper, claim frequency followed the Poisson distribution while claim severity followed the Lognormal distribution. Result of analysis showed that rate values based on claim frequency and severity are higher than the rate values that were used back in 2010.&lt;/p&gt;&lt;p&gt;&lt;strong&gt;Keywords&lt;/strong&gt;&lt;strong&gt;:&lt;/strong&gt; bayesian credibility; rate; claim frequency; claim severity&lt;/p&gt;

Underwriting information and insurers' profitability: Evidence from automobile physical damage insurance in Taiwan

The asymmetric learning hypothesis describes that an insurer can earn a higher profit by possessing underwriting information on repeat customers that is not available to other insurers. This study investigates whether this advantage is still sustained under a complete information-sharing mechanism. We employ data on automobile physical damage insurance in Taiwan to analyze whether insurers still enjoy an information advantage for repeat customers and whether they earn higher profits on staying policies. The findings reveal that switching and repeat customers do not affect insurers' profitability, suggesting that insurers do not have an information advantage over repeat customers; therefore, a complete information-sharing mechanism can eliminate asymmetric information among insurers. Moreover, the availability of abundant underwriting information enables insurers to more accurately assess customers' risk levels, which increases insurers' profitability. Furthermore, the results indicate that the bonus-malus system does not effectively reduce risks associated with policyholders with high claim frequencies because the degree of the increase in premium is lower than the increase in claim amounts, which is attributable to institutional factors. Our study implies the necessity of designing a more effective bonus-malus system in addition to underwriting screening.

Nonparametric intercept regularization for insurance claim frequency regression models

Abstract In a subgroup analysis for an actuarial problem, the goal is for the investigator to classify the policyholders into unique groups, where the claims experience within each group are made as homogenous as possible. In this paper, we illustrate how the alternating direction method of multipliers (ADMM) approach for subgroup analysis can be modified so that it can be more easily incorporated into an insurance claims analysis. We present an approach to penalize adjacent coefficients only and show how the algorithm can be implemented for fast estimation of the parameters. We present three different cases of the model, depending on the level of dependence among the different coverage groups within the data. In addition, we provide an interpretation of the credibility problem using both random effects and fixed effects, where the fixed effects approach corresponds to the ADMM approach to subgroup analysis, while the random effects approach represents the classic Bayesian approach. In an empirical study, we demonstrate how these approaches can be applied to real data using the Wisconsin Local Government Property Insurance Fund data. Our results show that the presented approach to subgroup analysis could provide a classification of the policyholders that improves the prediction accuracy of the claim frequencies in case other classifying variables are unavailable in the data.

Calculation of Motor Vehicle Insurance Premiums Through Evaluation of Claim Frequency and Amount Data

Insurance, as a risk control strategy by transferring the burden of risk from one party to another, consists of two main forms: life insurance, which covers financial losses from the risk of death of the policyholder, and general insurance, which involves the transfer of risk against property losses. Motor vehicle insurance has become a common product reflecting the high value and benefits of motor vehicles, which has resulted in an increase in vehicle ownership. Although the increase in the number of vehicles contributes to the increase in road accidents, many owners who suffer losses do not receive the compensation they deserve. In this context, the premium becomes a key factor, where the policyholder pays a certain amount of money to get protection. This research aims to apply risk premium calculation based on claim frequency and claim size data, as conducted by Ozgurel in 2005, especially for each vehicle category and region in XYZ insurance company. The main problem is to optimize the premium calculation to reflect the actual risk, providing a more accurate understanding of the influence of vehicle and regional characteristics in determining a fair and appropriate premium.

Perhitungan Premi Murni Kendaraan Bermotor Menggunakan Generalized Linear Models

Insurance is a form of agreement between the insurer against the insured party (insurance company), where the insurer will pay a premium to the insured every month as a form of collateral for loss or damage that befalls him for certain events. Researchers took data by distributing questionnaires to respondents. Some covariate variables used in the study include: gender, vehicle age, vehicle insurance costs, vehicle use, vehicle mileage every year, and claims records in the last three years. Meanwhile, the dependent variable is frequency claim and claim severity. The researcher estimates the Generalized Linear Models (GLZ) parameters using the maximum likelihood estimation (MLE). The next step, researchers conducted a model compatibility test on the dependent variable using calculations on the Akaike Information Criteria (AIC), where the model chosen was the model with the lowest AIC value. Based on this, the researcher can determine covariate variables that affect the dependent variable and model it. The final step is the researcher calculates the probability of claim frequency, claim severity, and estimates the amount of pure premiums charged to respondents.