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Quantifying Risk of Insurance Claims Data Using Various Loss Distributions |
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PP: 1031-1044 |
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doi:10.18576/jsap/130315
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Author(s) |
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Walena A. Marambakuyana,
Sandile C. Shongwe,
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Abstract |
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| This research work presents an empirical and theoretical discussion on the area of quantifying risk using parametric loss distributions to model insurance claims data. That is, this paper provides a large-scale comparison of 19 standard parametric distributions for curve-fitting using the South African taxi claims data and the Danish fire loss data. When a few standard loss distributions (to be exact, six, i.e., exponential, gamma, Weibull, lognormal, Pareto, and Burr) were considered for the taxi claims data, the lognormal and Pareto distributions were said to have the best fit for that insurance dataset. In this research work, the list of fitted standard distributions is extended from 6 to 19 (for taxi claims data), and it is observed that there are some standard distributions that provide a better fit than the lognormal and Pareto distributions for both datasets when evaluating the fit using goodness-of-fit measures and then compute their corresponding risk measures (i.e., value-at-risk (VaR) and tail value-at-risk (TVaR)). In general, when fitting the standard loss distributions to both datasets, the transformed beta family of distributions has the best fit, whereas the transformed gamma family of distributions provides the worst fit. Another observation is that the more parameters the distribution has, the more flexible the distribution is, and the better the fit to the data when compared to the other distributions in that parametric family. However, most of the fitted loss distributions tend to overestimate (or underestimate) the risk metrics which may lead to over-reserving (under-reserving), respectively.
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