Accident Severity Modelling & Ruin Probability

Overview

This project, an individual assignment for the ACTL3162 General Insurance course, tackles two fundamental areas of actuarial science: accident severity modeling and the analysis of ruin probability. The primary goal was to apply statistical and actuarial theories to analyze a dataset of motor insurance claims. All analysis, modeling, and computations were performed using the R programming language.

For more information, visit the project web page.

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How to Use

To replicate this project and run the analysis yourself, you will need to have R installed.

1. Clone the repository:

   git clone [https://github.com/quenstance/2019_ACTL3162_Accident_Severity_Modelling.git](https://github.com/quenstance/2019_ACTL3162_Accident_Severity_Modelling.git)

2. Navigate to the project directory and set your working directory in RStudio:

   #Set working directory to the location of the cloned repository
   setwd("C:/path/to/your/cloned/repo") 

3. Install the required R packages: Run the following commands in the R console to install the necessary libraries:

   install.packages("fitdistrplus")
   install.packages("actuar")
   install.packages("moments")
   install.packages("rSymPy")
   install.packages("rJava")
   install.packages("rootSolve")

4. Load packages: After installation, load the libraries by running:

   library(fitdistrplus)
   library(actuar)
   library(moments)
   library(rSymPy)
   library(rJava)
   library(rootSolve)

5. Run the script: Execute the R script files in the correct order as described in the report to reproduce the analysis and findings. The data.csv file should be included in the repository for the script to run.

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Methodology

The methodology for this project was structured into two main tasks:

• Task 1: Accident Severity Modeling: This involved using Maximum Likelihood Estimation (MLE) to fit various distributions (e.g., Gamma, Lognormal, and Burr) to claims data. The model selection process was comprehensive, combining a graphical approach (using Cullen and Frey graphs, Q-Q plots, and P-P plots) with statistical tests like the Anderson-Darling, Kolmogorov-Smirnov, and Cramér-von Mises tests, along with the AIC and BIC information criteria.
• Task 2: Ruin Theory: This task involved applying ruin theory to a simple surplus model, examining scenarios with and without insurance, as well as with both proportional and non-proportional reinsurance. A key part of this task also involved implementing the Panjer recursion method to perform convolution and approximate the distribution of aggregated claims.

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Key Finding

The project yielded several important findings:

• The Gamma distribution was identified as the most suitable model for the claims data, outperforming other distributions in statistical tests and effectively capturing the crucial tail risk of the distribution.
• A deeper analysis of the more complex Burr distribution revealed a high correlation in bootstrapped parameters, suggesting that its additional parameters might not offer significant value.
• The analysis demonstrated that non-proportional reinsurance was more effective than proportional reinsurance at increasing the adjustment coefficient, thus improving solvency.
• The implementation of Panjer recursion successfully produced numerical results that were very close to the true values, validating the chosen approximation method.

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Limitation

The project was subject to several constraints:

• The dataset consisted of just over 1,000 claims from a single motor insurance product, which may limit the generalizability of the findings.
• The process of finding appropriate initial conditions for the MLE optimization was noted as being challenging.
• The continuous model for ruin probability proved to be computationally intensive and susceptible to numerical instability when calculating values for larger time horizons.

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Author

• Quenstance Lau
• Web Portfolio: https://quenstance.pages.dev/projects/accident-severity-model/
• LinkedIn: [https://www.