Risk measures associated with insurance losses in Ghana

Value-at-risk (VaR) and tail value-at-risk (TVaR) have been used extensively in the financial sector to estimate the worst possible losses for a given portfolio. However, not much has been done to apply these concepts in insurance. It is particularly useful to know, on average, the largest possible claim an insurance company can pay in order to readjust its annual premium rate for compensating possible losses. To this end, this study estimates the VaR and TVaR of comprehensive motor insurance losses (claims) paid by an insurance company in Ghana. In order to identify which continuous distribution function best fits our data, we fit our data to a number of different continuous distributions and then test their goodness-of-fit using the Kolmogorov– Smirnov test. The lognormal distribution is the best fit to our data. VaR and TVaR are then estimated using the lognormal distribution function. Analysis of variance is used to check if there are statistically significant differences between the estimates obtained from both risk measures. Given the vast difference in the estimates provided by both risk measures, it is essential for actuaries to critically assess the type of risk measure used when advocating for reinsurance.