ESTIMATING LOSS SEVERITY DISTRIBUTION: CONVOLUTION APPROACH

Abstract

Financial loss can be classified into two types such as expected loss and unexpected loss. A current definition seeks to separate two losses from a total loss. In this article, however, we redefine a total loss as the sum of expected and unexpended losses; then the distribution of loss can be considered as the convolution of the distributions of both expected and unexpended losses. We propose to use a convolution of normal and exponential distribution for modelling a loss distribution. Subsequently, we compare its performance with other commonly used loss distributions. The examples of property insurance claim data are analyzed to show the applicability of this normal-exponential convolution model. Overall, we claim that the proposed model provides further useful information with regard to losses compared to existing models. We are able to provide new statistical quantities which are very critical and useful.