Search Results (12)

This study addresses key challenges in auto insurance territory risk analysis by examining the complexities of spatial loss data and the evolving landscape of territorial risks before and during the COVID-19 pandemic. Traditional approaches, such as spatial clustering, are commonly used for territory risk assessment but offer limited predictive capabilities, constraining their effectiveness in forecasting future losses, an essential component of insurance pricing. To overcome this limitation, we propose an advanced predictive modeling framework that integrates spatial loss patterns while accounting for the pandemic’s impact. Our Bayesian-based spatial model captures stochastic spatial autocorrelations among territory rating units and their neighboring regions. This approach enables more robust pattern recognition through predictive modeling. By applying this approach to regulatory auto insurance loss datasets, we analyze industry-level trends in claim frequency, loss severity, loss cost, and insurance loading. The results reveal significant shifts in spatial loss patterns before and during the pandemic, highlighting the dynamic interplay between regional risk factors and external disruptions. These insights provide valuable guidance for insurers and regulators, facilitating more informed decision-making in risk classification, pricing adjustments, and policy interventions in response to evolving spatial and economic conditions. Full article

This study examines how telematics variables such as annual percentage driven, total miles driven, and driving patterns influence the distributional behaviour of conventional rating factors when incorporated into predictive models for capturing auto insurance risk in rate regulation. To effectively manage the complexity inherent in telematics data, we advocate for the adoption of non-negative sparse principal component analysis (NSPCA) as a structured approach for data dimensionality reduction. By emphasizing sparsity and non-negativity constraints, NSPCA enhances the interpretability and predictive power of models concerning both loss severity and claim counts. This methodological innovation aims to advance statistical analyses within insurance pricing frameworks, ensuring the robustness of predictive models and providing insights crucial for rate regulation strategies specific to the auto insurance sector. Results show that, to enhance auto insurance risk pricing models, it is essential to address data dimension reduction challenges when integrating telematics data variables. Our findings underscore that integrating telematics variables into predictive models maintains the integrity of risk relativity estimates associated with traditional policy variables. Full article

This research delves into the fusion of spatial clustering and predictive modeling within auto insurance data analytics. The primary focus of this research is on addressing challenges stemming from the dynamic nature of spatial patterns in multiple accident year claim data, by using spatially constrained clustering. The spatially constrained clustering is implemented under hierarchical clustering with a soft contiguity constraint. It is highly desirable for insurance companies and insurance regulators to be able to make meaningful comparisons of loss patterns obtained from multiple reporting years that summarize multiple accident year loss metrics. By integrating spatial clustering techniques, the study not only improves the credibility of predictive models but also introduces a strategic dimension reduction method that concurrently enhances the interpretability of predictive models used. The evolving nature of spatial patterns over time poses a significant barrier to a better understanding of complex insurance systems as these patterns transform due to various factors. While spatial clustering effectively identifies regions with similar loss data characteristics, maintaining up-to-date clusters is an ongoing challenge. This research underscores the importance of studying spatial patterns of auto insurance claim data across major insurance coverage types, including Accident Benefits (AB), Collision (CL), and Third-Party Liability (TPL). The research offers regulators valuable insights into distinct risk profiles associated with different coverage categories and territories. By leveraging spatial loss data from pre-pandemic and pandemic periods, this study also aims to uncover the impact of the COVID-19 pandemic on auto insurance claims of major coverage types. From this perspective, we observe a statistically significant increase in insurance premiums for CL coverage after the pandemic. The proposed unified spatial clustering method incorporates a relabeling strategy to standardize comparisons across different accident years, contributing to a more robust understanding of the pandemic effects on auto insurance claims. This innovative approach has the potential to significantly influence data visualization and pattern recognition, thereby improving the reliability and interpretability of clustering methods. Full article

This study delves into a critical examination of the Size of Loss distribution patterns in the context of auto insurance during pre- and post-pandemics, emphasizing their profound influence on insurance pricing and regulatory frameworks. Through a comprehensive analysis of the historical Size of Loss data, insurers and regulators gain essential insights into the probabilities and magnitudes of insurance claims, informing the determination of precise insurance premiums and the management of case reserving. This approach aids in fostering fair competition, ensuring equitable premium rates, and preventing discriminatory pricing practices, thereby promoting a balanced insurance landscape. The research further investigates the impact of the COVID-19 pandemic on these Size of Loss patterns, given the substantial shifts in driving behaviours and risk landscapes. Also, the research contributes to the literature by addressing the need for more studies focusing on the implications of the COVID-19 pandemic on pre- and post-pandemic auto insurance loss patterns, thus offering a holistic perspective encompassing both insurance pricing and regulatory dimensions. Full article

Territory risk analysis has played an important role in auto insurance rate regulation. It aims to design rating territories from a set of basic rating units so that their respective risk relativities can be estimated to reflect the regional risk of insurance. In this work, spatially constrained clustering is first applied to insurance loss data to form such regions, using the forward sortation area (FSA) as a basic rating unit. The groupings of FSA by spatially constrained clustering reduce the insurance rate heterogeneity caused by smaller risk exposures. Furthermore, the generalized linear mixed model (GLMM) is proposed to derive the risk relativities of clusters and each FSA. In addition, as an alternative approach, fuzzy C-Means clustering is proposed to derive the risk relativity of FSA, and the obtained results are compared to the ones from GLMM. The spatially constrained clustering and risk relativity estimation help to retrieve a set of territory risk benchmarks used in rate filings within the regulation process. It also provides guidance for auto insurance companies on rate making. Full article

Pricing using a Generalised Linear Model is the gold standard in the auto insurance industry and rate regulation. Generalised Additive Model applications in insurance pricing are receiving increasing attention from academic researchers and actuarial pricing professionals. The actuarial practice has constantly shown evidence of significantly different premium rates among the different rating territories. In this work, we build predictive models for claim frequency and severity using the synthetic Usage Based Insurance (UBI) dataset variables. First, we conduct territorial clustering based on each location’s claim counts and amounts by grouping those locations into a smaller set, defined as a cluster for rating purposes. After clustering, we incorporate these clusters into our predictive model to determine the risk relativity for each factor level. Through predictive modelling, we have successfully identified key factors that may be helpful for the rate regulation of UBI. Our work aims to fill the gap between individual-level pricing and rate regulation using the UBI database and provides insights on consistency in using traditional rating variables for UBI pricing. Our main contribution is to outline how GAM can address a more complicated functionality of risk factors and the interactions among them. We also contribute to demonstrating the territory clustering problem in UBI to construct the rating territories for pricing and rate regulation. We find that relativity for high annual mileage driven is almost three times that associated with low annual mileage level, which implies its importance in premium calculation. Overall, we provide insights into how UBI can be regulated through traditional pricing factors, additional factors from UBI datasets and rating territories derived from basic rating units and the driver’s location. Full article

The study of actuarial fairness in auto insurance has been an important issue in the decision making of rate regulation. Risk classification and estimating risk relativities through statistical modeling become essential to help achieve fairness in premium rates. However, because of minor adjustments to risk relativities allowed by regulation rules, the rates charged eventually may not align with the empirical risk relativities calculated from insurance loss data. Therefore, investigating the relationship between the premium rates and loss costs at different risk factor levels becomes important for studying insurance fairness, particularly from rate regulation perspectives. This work applies statistical models to rate and classification data from the automobile statistical plan to investigate the disparities between insurance premiums and loss costs. The focus is on major risk factors used in the rate regulation, as our goal is to address fairness at the industry level. Various statistical models have been constructed to validate the suitableness of the proposed methods that determine a fixed effect. The fixed effect caused by the disparity of loss cost and premium rates is estimated by those statistical models. Using Canadian data, we found that there are no significant excessive premiums charged at the industry level, but the disparity between loss cost and premiums is high for urban drivers at the industry level. This study will help better understand the extent of auto insurance fairness at the industry level across different insured groups characterized by risk factor levels. The proposed fixed-effect models can also reveal the overall average loss ratio, which can tell us the fairness at the industry level when compared to loss ratios by the regulation rules. Full article

Predictive modeling is a critical technique in many real-world applications, including auto insurance rate-making and the decision making of rate filings review for regulation purposes. It is also important in predicting financial and economic risk in business and economics. Unlike testing hypotheses in statistical inference, results obtained from predictive modeling serve as statistical evidence for the decision making of the underlying problem and discovering the functional relationship between the response variable and the predictors. As a result of this, the variable importance measures become an essential aspect of helping to better understand the contributions of predictors to the built model. In this work, we focus on the study of using generalized linear models (GLM) for the size of loss distributions. In addition, we address the problem of measuring the importance of the variables used in the GLM to further evaluate their potential impact on insurance pricing. In this regard, we propose to shift the focus from variable importance measures of factor levels to factors themselves and to develop variable importance measures for factors included in the model. Therefore, this work is exclusively for modeling with categorical variables as predictors. This work contributes to the further development of GLM modeling to make it even more practical due to this added value. This study also aims to provide benchmark estimates to allow for the regulation of insurance rates using GLM from the variable importance aspect. Full article

This study analyses the long- and short-term dynamics of the determinants of insurance penetration for the period 1999Q1 to 2019Q4 in 15 West African countries. The panel auto regressive distributed lag model was used on the quarterly data gathered. A cointegrating and short-run momentous connection was discovered between insurance penetration along with the independent variables, which were education, productivity, dependency, inflation and income. The error correction term’s significance and negative sign demonstrate that all variables are heading towards long-run equilibrium at a moderate speed of 56.4%. This further affirms that education, productivity, dependency, inflation and income determine insurance penetration in West Africa in the long run. In addition, the short-run causality revealed that all the pairs of regressors could jointly cause insurance penetration. The findings of this study recommend that the economy-wide policies by the government and the regulators of insurance markets in these economies should be informed by these significant factors. The restructuring of the education sector to ensure finance-related modules cut across every faculty in the higher education sector is also recommended. Furthermore, Bancassurance is also recommended to boost the easy penetration of the insurance sector using the relationship with the banking sector as a pathway. Full article

In insurance rate-making, the use of statistical machine learning techniques such as artificial neural networks (ANN) is an emerging approach, and many insurance companies have been using them for pricing. However, due to the complexity of model specification and its implementation, model explainability may be essential to meet insurance pricing transparency for rate regulation purposes. This requirement may imply the need for estimating or evaluating the variable importance when complicated models are used. Furthermore, from both rate-making and rate-regulation perspectives, it is critical to investigate the impact of major risk factors on the response variables, such as claim frequency or claim severity. In this work, we consider the modelling problems of how claim counts, claim amounts and average loss per claim are related to major risk factors. ANN models are applied to meet this goal, and variable importance is measured to improve the model’s explainability due to the models’ complex nature. The results obtained from different variable importance measurements are compared, and dominant risk factors are identified. The contribution of this work is in making advanced mathematical models possible for applications in auto insurance rate regulation. This study focuses on analyzing major risks only, but the proposed method can be applied to more general insurance pricing problems when additional risk factors are being considered. In addition, the proposed methodology is useful for other business applications where statistical machine learning techniques are used. Full article

Territory design and analysis using geographical loss cost are a key aspect in auto insurance rate regulation. The major objective of this work is to study the design of geographical rating territories by maximizing the within-group homogeneity, as well as maximizing the among-group heterogeneity from statistical perspectives, while maximizing the actuarial equity of pure premium, as required by insurance regulation. To achieve this goal, the spatially-constrained clustering of industry level loss cost was investigated. Within this study, in order to meet the contiguity, which is a legal requirement on the design of geographical rating territories, a clustering approach based on Delaunay triangulation is proposed. Furthermore, an entropy-based approach was introduced to quantify the homogeneity of clusters, while both the elbow method and the gap statistic are used to determine the initial number of clusters. This study illustrated the usefulness of the spatially-constrained clustering approach in defining geographical rating territories for insurance rate regulation purposes. The significance of this work is to provide a new solution for better designing geographical rating territories. The proposed method can be useful for other demographical data analysis because of the similar nature of the spatial constraint. Full article

Predictive modeling is a key technique in auto insurance rate-making and the decision-making involved in the review of rate filings. Unlike an approach based on hypothesis testing, the results from predictive modeling not only serve as statistical evidence for decision-making, they also discover relationships between a response variable and predictors. In this work, we study the use of predictive modeling in auto insurance rate filings. This is a typical area of actuarial practice involving decision-making using industry loss data. The aim of this study was to offer some general guidelines for using predictive modeling in regulating insurance rates. Our study demonstrates that predictive modeling techniques based on generalized linear models (GLMs) are suitable in auto insurance rate filings review. The GLM relativities of major risk factors can serve as the benchmark of the same risk factors considered in auto insurance pricing. Full article