Determining Premium In An Excess-Of-Loss Reinsurance Contract -An Extreme Value Approach

Abstract

Statistics of extremes deals with the estimation of rare events that may have catastrophic effects on life, environment, among others. Since the introduction of Extreme value theory (EVT), it has been used in modelling various extreme events in fields such as finance, insurance, transportation, etc. In this thesis, the EVT is applied to model two claims datasets from the Ghanaian insurance industry. To do this, we employ the Peak Over Threshold (POT) method using the splicing Generalized Pareto Distribution (GPD) in modelling the tails of the underlying distributions. The primordial parameter in the estimation of extreme events is the tail index or Extreme Value Index (EVI). The EVI enables the classification of the underlying distribution of a dataset into three family of distributions that have short, light, or heavy tails. Thereafter, any of the parameters of extremes such as extreme quantiles, small exceedance probabilities, right endpoints and return periods can be estimated. Excess Loss Premium (XLP), Expected Shortfall (ES) and Value at Risk (VaR) as risk measures were thereafter calculated through the splicing method. The impact of the extreme value index (EVI) on these risk measures for the two datasets are discussed and suggestions made on how these could help the primary insurer in limiting the danger of large claims on the solvency of these companies. Based on this, the insurance companies can assess the risk associated with large claims and transfer some of these risks to reinsurance companies given their retention level. This study recommends that the splicing method should be used in fitting insurance data which behaves differently at various intervals of claims amount.