Inflation Index for the House and Content Portfolio : A Model to Calculate the Future Claim Costs for Trygg-Hansa

Sammanfattning: Trygg-Hansa is a Swedish insurance company that specializes in business insurance, home insurance, vehicle insurance, and personal insurance. This work focuses on Trygg-Hansa’s House and Content portfolio, which insures customers’ homes, both the building itself and its contents. In the event of damage or accidents, the company compensates customers financially, but due to rising inflation, these expenses have become increasingly expensive.  Today, Trygg-Hansa has a model for predicting the future cost of compensate damages within the House and Content portfolio, but sees a great need to develop it further. The goal of this work is to find a better model for predicting future costs and to create an inflation index. This index can serve as a basis for the pricing department, as it can be used to adjust customers’ premiums to maintain a profitable business.  The data was collected from the company’s systems, and nine data sets were created, one for each type of damage. The models used to predict the future claim costs were Autoregressive Integrated Moving Average (ARIMA), Seasonal Autoregressive Integrated Moving Average (SARIMA), and Exponential Smoothing (ES). Each claim type was predicted two years ahead, and thereafter the Laspeyres Price Index was calculated. This was done for all three models, and then the results of the models were compared.  The models were trained for the years 2013-2021, while the years 2021-2023 were used to evaluate the models. All types of damage had rising costs between 2013- 2021, but at the beginning of 2021 and forwards, the trends changed to decreasing trends for almost all types of damage. This affected the results of the models, as they were only trained on rising trends, and therefore, the forecast evaluation (Root Mean Squared Error and Mean Average Percent Error) was not useful. The ARIMA and SARIMA models showed almost no trends in the predicted data. This may be due to too complex data with too much volatility and unclear trends for the implemented module.  The Exponential Smoothing model follows the historical data both trend-wise and with a likely seasonal pattern for all nine types of damage and for the historical LPI. The forecast made by the ES and SARIMA models also show similar seasonal patterns. Furthermore, the ES model has the best model fit according to the Box-Jenkins Diagnostic. The model may need to be corrected in a year when the declining trend has been included in the training data by setting more weight to the new data for the year 2021.