Determining Premium In An Excess-Of-Loss Reinsurance Contract -An Extreme Value Approach
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Date
2022-06
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University Of Ghana
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.
Description
MPhil. Actuarial Science
Keywords
Reinsurance Contract, Premium