Abstract
Traditional loss reserves models focus on the mean of the conditional loss distribution. If the factors driving high claims differ systematically from those driving medium to low claims, alternative models that differentiate such differences are required. We propose quantile regression model loss reserving as the model offers potentially different solutions at distinct quantiles so that the effects of risk factors are differentiated at different points of the conditional loss distribution. Due to its nonparametric nature, quantile regression is free of the model assumptions for traditional mean regression models, including homogeneous variance across risk factors and symmetric and light tails, etc. These model assumptions have posed a great barrier in applications as they are often not met in the claim data. Using two sets of run-off triangle claim data from Israel and Queensland, Australia, we present the quantile regression approach that illustrates the sensitivity of claim size to risk factors, namely the trend pattern and initial claim level, in different quantiles. Trained models are applied to predict future claims in the lower run-off triangle. Findings suggest that reliance on standard loss reserves techniques gives rise to misleading inferences and that claim size is not homogeneously driven by the same risk factors across quantiles.
Highlights
An insurance company promises to pay claims to the insureds if some defined events occur
As insurers receive premiums from policyholders in advance to pay for the future claims on losses specified in insurance contracts in return, they must have the necessary loss reserves to pay for these outstanding claims and settlement costs incurred
The model is applied to two loss reserves data and results illustrate that the claim levels in different quantiles show significantly different trend patterns across lag-period and different sensitivities to initial claim level or exposure
Summary
An insurance company promises to pay claims to the insureds if some defined events (injury, accident, death, etc.) occur. Failure to include all relevant variables often occurs because of insufficient knowledge of the many underlying risk factors that drive the claim process or the inability to measure all relevant processes This is the case when aggregate instead of individual claims are modelled. Quantile regression in insurance applications can be found in Portnoy [21] for the graduation of mortality table rates, Pitt [20] for the claim termination rates for income protection insurance and Kudryavtsev [19] for rate-making in heterogeneous insurance portfolios None of these works focus on loss reserve models for run-off triangle using the trend of claims to predict future claims.
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