This work separately models claim frequency and severity to investigate the application of Generalised Linear Models (GLMs) to estimate the pure premium in auto insurance. We show how transparent, data-driven methods can support fair and efficient pricing in a regulated sector using an open dataset from Kaggle and repeatable R code.
Table of Contents
- 1. Introduction
- 2. Literature Review
- 2.1 Definition of Pure Premium
- 2.2 Overview of Generalized Linear Models (GLMs) in Actuarial Science
- 2.3 Typical Distributions for Frequency and Severity
- 2.4 Pricing Models Using GLMs in R
- 2.5 Advances in Actuarial Modeling and Reproducibility
- 3. Methodology
- 3.1 Data Description
- 3.2 Modeling Claim Frequency
- 3.3 Modeling Claim Severity
- 3.4 Calculating the Pure Premium
- 3.5 Evaluation Metrics and Visualization
- 4. Results
- 4.1 Frequency Model Results (Poisson GLM)
- 4.2 Severity Model Results (Gamma GLM with Log Link)
- 4.3 Estimated Pure Premium by Segment
- 4.4 Visualizations
- 5. Discussion and Interpretation
- 5.1 Interpretation of Frequency and Severity Results
Objectives and Key Themes
This paper aims to provide a reproducible case study on estimating pure premium in auto insurance using Generalized Linear Models (GLMs) and the R programming language. It demonstrates the application of transparent, data-driven methods for fair and efficient pricing within a regulated sector, using an open dataset. The study emphasizes the importance of reproducibility in actuarial modeling.
- Application of GLMs to auto insurance pricing
- Frequency-severity modeling approach
- Reproducibility and transparency in actuarial modeling
- Use of R for data analysis and model implementation
- Interpretability of GLM-based pricing models
Chapter Summaries
1. Introduction: This chapter establishes the context of accurate pricing in auto insurance, highlighting the importance of the pure premium as a key component. It introduces the frequency-severity method for decomposing expected loss cost, enabling separate modeling strategies for claim frequency and severity. The chapter also emphasizes the use of Generalized Linear Models (GLMs) in actuarial science, their flexibility in handling various data types, and their increasing importance in meeting regulatory expectations for transparency and explainable pricing. Finally, it introduces the paper's objectives, focusing on a reproducible R-based approach to estimating pure premium using real-world data.
2. Literature Review: This chapter provides a comprehensive overview of existing literature relevant to the study. It delves into the definition of pure premium, examines the application and theoretical underpinnings of Generalized Linear Models (GLMs) within the field of actuarial science, and explores typical distributions used for modeling claim frequency (Poisson, Negative Binomial) and severity (Gamma, Log-Normal). The review also discusses the use of GLMs in R for pricing models, highlighting the advantages of using R for reproducible research in actuarial settings. Finally, it likely touches on recent advancements in actuarial modeling techniques and the growing emphasis on reproducible research methods.
3. Methodology: This chapter details the methodology employed in the study, starting with a description of the dataset utilized. It outlines the statistical models used to analyze claim frequency and severity. This section would cover the specific GLMs applied (e.g., Poisson GLM for frequency, Gamma GLM for severity), along with the choice of link functions. The chapter then explains how the pure premium is calculated by combining the frequency and severity models and specifies the evaluation metrics used to assess model performance, including the visualization techniques utilized to present the results.
4. Results: This chapter presents the findings from the statistical modeling and analysis, detailing the results of the frequency model (Poisson GLM) and the severity model (Gamma GLM with log link). It likely includes key performance indicators for each model and their interpretations. A crucial aspect of this chapter is the presentation of estimated pure premium by different insured segments. The chapter concludes with a discussion of visualizations used to present the modeling results, enhancing understanding and interpretation.
5. Discussion and Interpretation: This chapter provides an interpretation of the results obtained from the frequency and severity models, exploring the implications of the findings. This section would likely discuss the limitations of the models, the robustness of the findings, and potential areas for future research. It might also discuss any significant insights gleaned from the modeling process and connect these insights back to the overall objectives of the study.
Keywords
Auto Insurance, Pure Premium, GLM, Frequency-Severity Modeling, R, Reproducibility, Risk Segmentation
Table of Contents
- 1. Introduction
- 2. Literature Review
- 2.1 Definition of Pure Premium
- 2.2 Overview of Generalized Linear Models (GLMs) in Actuarial Science
- 2.3 Typical Distributions for Frequency and Severity
- 2.4 Pricing Models Using GLMs in R
- 2.5 Advances in Actuarial Modeling and Reproducibility
- 3. Methodology
- 3.1 Data Description
- 3.2 Modeling Claim Frequency
- 3.3 Modeling Claim Severity
- 3.4 Calculating the Pure Premium
- 3.5 Evaluation Metrics and Visualization
- 4. Results
- 4.1 Frequency Model Results (Poisson GLM)
- 4.2 Severity Model Results (Gamma GLM with Log Link)
- 4.3 Estimated Pure Premium by Segment
- 4.4 Visualizations
- 5. Discussion and Interpretation
- 5.1 Interpretation of Frequency and Severity Results
Objectives and Key Themes
This paper aims to provide a reproducible case study on estimating pure premium in auto insurance using Generalized Linear Models (GLMs) and the R programming language. It demonstrates the application of transparent, data-driven methods for fair and efficient pricing within a regulated sector, using an open dataset. The study emphasizes the importance of reproducibility in actuarial modeling.
- Application of GLMs to auto insurance pricing
- Frequency-severity modeling approach
- Reproducibility and transparency in actuarial modeling
- Use of R for data analysis and model implementation
- Interpretability of GLM-based pricing models
Chapter Summaries
1. Introduction: This chapter establishes the context of accurate pricing in auto insurance, highlighting the importance of the pure premium as a key component. It introduces the frequency-severity method for decomposing expected loss cost, enabling separate modeling strategies for claim frequency and severity. The chapter also emphasizes the use of Generalized Linear Models (GLMs) in actuarial science, their flexibility in handling various data types, and their increasing importance in meeting regulatory expectations for transparency and explainable pricing. Finally, it introduces the paper's objectives, focusing on a reproducible R-based approach to estimating pure premium using real-world data.
2. Literature Review: This chapter provides a comprehensive overview of existing literature relevant to the study. It delves into the definition of pure premium, examines the application and theoretical underpinnings of Generalized Linear Models (GLMs) within the field of actuarial science, and explores typical distributions used for modeling claim frequency (Poisson, Negative Binomial) and severity (Gamma, Log-Normal). The review also discusses the use of GLMs in R for pricing models, highlighting the advantages of using R for reproducible research in actuarial settings. Finally, it likely touches on recent advancements in actuarial modeling techniques and the growing emphasis on reproducible research methods.
3. Methodology: This chapter details the methodology employed in the study, starting with a description of the dataset utilized. It outlines the statistical models used to analyze claim frequency and severity. This section would cover the specific GLMs applied (e.g., Poisson GLM for frequency, Gamma GLM for severity), along with the choice of link functions. The chapter then explains how the pure premium is calculated by combining the frequency and severity models and specifies the evaluation metrics used to assess model performance, including the visualization techniques utilized to present the results.
4. Results: This chapter presents the findings from the statistical modeling and analysis, detailing the results of the frequency model (Poisson GLM) and the severity model (Gamma GLM with log link). It likely includes key performance indicators for each model and their interpretations. A crucial aspect of this chapter is the presentation of estimated pure premium by different insured segments. The chapter concludes with a discussion of visualizations used to present the modeling results, enhancing understanding and interpretation.
5. Discussion and Interpretation: This chapter provides an interpretation of the results obtained from the frequency and severity models, exploring the implications of the findings. This section would likely discuss the limitations of the models, the robustness of the findings, and potential areas for future research. It might also discuss any significant insights gleaned from the modeling process and connect these insights back to the overall objectives of the study.
Keywords
Auto Insurance, Pure Premium, GLM, Frequency-Severity Modeling, R, Reproducibility, Risk Segmentation
Frequently asked questions
What is the main objective of the "Pure Premium Estimation in Auto Insurance using GLMs" paper?
The paper aims to provide a reproducible case study demonstrating how to estimate pure premium in auto insurance using Generalized Linear Models (GLMs) and the R programming language. It highlights transparent, data-driven methods for fair and efficient pricing within a regulated sector, utilizing an open dataset and emphasizing reproducibility in actuarial modeling.
What is pure premium and why is it important?
Pure premium is a key component of auto insurance pricing, representing the expected loss cost. It's crucial for accurate pricing, ensuring that insurance companies can cover expected claims while remaining competitive.
What is the frequency-severity method?
The frequency-severity method is a way of decomposing expected loss cost into two components: claim frequency (how often claims occur) and claim severity (the cost of each claim). This allows for separate modeling strategies for each component.
What are Generalized Linear Models (GLMs) and why are they used in this context?
Generalized Linear Models (GLMs) are a flexible class of statistical models that can handle various data types. They are used in actuarial science for their ability to model non-normal data and for their increasing importance in meeting regulatory expectations for transparency and explainable pricing.
What distributions are typically used for modeling claim frequency and severity?
Typical distributions used for modeling claim frequency include Poisson and Negative Binomial. For claim severity, Gamma and Log-Normal distributions are commonly used.
What is the role of R in this study?
R is used for data analysis and model implementation. The paper emphasizes a reproducible R-based approach to estimating pure premium, highlighting the advantages of R for reproducible research in actuarial settings.
What is the methodology used in the study?
The methodology involves describing the dataset, modeling claim frequency (using a Poisson GLM), modeling claim severity (using a Gamma GLM), calculating the pure premium by combining the frequency and severity models, and using evaluation metrics and visualizations to assess model performance and present the results.
What are some key themes of the paper?
Key themes include the application of GLMs to auto insurance pricing, the frequency-severity modeling approach, reproducibility and transparency in actuarial modeling, the use of R for data analysis and model implementation, and the interpretability of GLM-based pricing models.
What does the Results chapter cover?
The Results chapter details the findings from the statistical modeling and analysis, including the results of the frequency model (Poisson GLM) and the severity model (Gamma GLM with log link). It presents key performance indicators for each model, estimated pure premium by different insured segments, and visualizations used to present the modeling results.
What topics are covered in the Literature Review chapter?
The Literature Review covers the definition of pure premium, an overview of Generalized Linear Models (GLMs) in actuarial science, typical distributions for frequency and severity, pricing models using GLMs in R, and advances in actuarial modeling and reproducibility.
- Quote paper
- Nabil Nakbi (Author), 2025, Pure Premium in Auto Insurance. A Reproducible Case Study Using R, Munich, GRIN Verlag, https://www.grin.com/document/1595608
