Extreme Value Theory Of Flood Losses
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Date
2018-09
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KNUST
Abstract
levels for the next 50,60 and 60 observations return levels were estimated and for the next 2 Extreme value theory is used in recent times in most risk management fields for large risks and predictions so as to prepare sufficiently for these losses. This thesis provides an overview of the theory as a method for modelling and measuring extreme risks. There are two main models of extreme value theory. The older Block Maxima method and the more recent Peaks Over Threshold. The Peaks Over Threshold method is favoured over the older Block Maxima method because it provides a simpler tool for estimating tail risks and uses data more efficiently considering the rarity of extreme data. Two types of data sets were used. One is a simulated flood insurance claim data and the other being losses due to flooding in the Kumasi Metropolitan Assembly. The method of maximum likelihood is used to estimate the shape and scale parameters of the generalized pareto distribution, which is a natural model for the excess distribution over a high threshold. The mean residual life plot is employed and used along with the quantile-quantile plots to aid in the selection of threshold. Two risk measures required from the objectives of the study were estimated as well as the return levels and return periods of the extremes. For the simulated insurance claim data, the value at risk results obtained at the 95th and 99th quatiles were GHC58,33.40 and GHC88,270.7 respectively, while results were also obtained for the flood losses data. The expected shortfalls for the corresponding value at risks were also obtained. The return levels obtained from the data included m-observation return levels and n-year return levels. Only m-observation was obtained for the simulated data because it was not simulated in yearly sets. For the next 500, 600 and 700, the return levels were GHC159,477.02, GHC172,149.37 and GHC183,878.28 respectively. Similarly for the flood losses data which were recorded on yearly basis, return,3 and 4 years, expected return levels were GHC1,438,058.75 GHC1,891,37065 and GHC2,285,39.43 respectively. The theory proved to be a good model for the measurement of extremes in
insurance and other areas.
Description
A THESIS SUBMITTED TO THE DEPARTMENT OF MATHEMATICS,KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY INPARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE MASTERS OF PHILOSOPHY IN ACTUARIAL SCIENCE