Louise Lindström: Development of Exposure Curves Within Reinsurance

Abstract.

This thesis examines the impact of exposure curves in the field of reinsurance. Specifically, it focuses on excess of loss contracts, where an insurance company only covers losses up to a predetermined threshold known as the retention. Any losses exceeding this threshold are then covered by a reinsurance company. The insurance company’s portfolio consists of objects with insured values and Estimated Maximum Loss (EML) values, which are determined by the insurance company. This information is then summarized into something called risk profiles, which in short is a overview of the insured objects within the insurance company.

If the EML value is below the retention, the insurance company bears full responsibility for any losses associated with that object. However, if the EML value exceeds the retention limit, both the insurance company and the reinsurance company face potential losses. Therefore, exposure is defined as the portion of risk that the insurance company is exposed to. An exposure curve is therefore a graphical representation of the relationship between the percentage of expected losses (y-axis) to the insurance company and different levels of exposure (x-axis).

This study explores two methods for constructing exposure curves: one using the distribution function of the degree of damage as input. The degree of damage is calculated by dividing the individual loss amount by its corresponding EML value. The other method is using the MBBEFD two-parameter function. Various methods for fitting the two parameters in the MBBEFD framework are performed. Then a comprehensive statistical analysis is conducted to estimate future losses, the number of losses and reinsurance premiums using exposure curves, risk profiles and excess of loss contracts. This is done by using both a fitted exposure curve and a standard exposure curve from Swiss Re. The results are then compared to each other.