An Analysis and forecast of the motor private insurance claim amounts in Kenya using the ARIMA model

Abstract

General insurance companies that offer motor private insurance packages face the need to hold enough reserves in order to meet any future claims liabilities. This involves carrying out a forecast of the future possible claims experiences to get an idea of the expected outflow of money from the business. In an attempt to achieve this, actuaries in Kenya turn to the commonly used actuarial forecasting techniques, which are the Chain Ladder Method and the Bornhuetter-Ferguson method. In as much as these methods are deemed simplistic and straightforward, they are not flexible and may be prone to distortion if at all the claims reporting pattern changes. By utilizing time series analysis and forecasting techniques, particularly the ARIMA model, the study seeks to offer a more flexible and accurate approach to forecasting insurance claims. This study explores the use of the ARIMA model as one of the methods that can be used to forecast motor private insurance claims in Kenya specifically focusing on the motor private claims amount data for the top five general insurance companies by market share: Old Mutual General Insurance, APA General Insurance, GA Insurance, CIC General Insurance, and Britam General Insurance. Using secondary data from the Insurance Regulatory Authority (IRA) spanning 2013 to 2022, the study gives the descriptive characteristics of the data and identifies an optimal order of the ARIMA model for each of the five companies: UAP with ARIMA(1,1,1), APA General Insurance with ARIMA(1,1,2), GA with ARIMA(0,1,1), CIC General Insurance with ARIMA(0,1,1), and lastly Britam General Insurance with ARIMA(0,1,1).The test for the accuracy using the Ljung-Box test after the forecast is generated for the period 2023 to 2027 reveals that the optimal order of the ARIMA model for each of the companies is indeed a good fit for the respective data. This suggests that actuaries can adopt time series analysis and forecasting techniques, most especially the ARIMA models, when performing forecasts of claim amounts within the actuarial space.