Research Article Open Access

ESTIMATING LOSS SEVERITY DISTRIBUTION: CONVOLUTION APPROACH

Ro J. Pak1
  • 1 Dankook University, Korea

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.

Journal of Mathematics and Statistics
Volume 10 No. 2, 2014, 247-254

DOI: https://doi.org/10.3844/jmssp.2014.247.254

Submitted On: 21 April 2014 Published On: 2 May 2014

How to Cite: Pak, R. J. (2014). ESTIMATING LOSS SEVERITY DISTRIBUTION: CONVOLUTION APPROACH. Journal of Mathematics and Statistics, 10(2), 247-254. https://doi.org/10.3844/jmssp.2014.247.254

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Keywords

  • Convolution
  • Heavy-Tailed Distribution
  • Loss
  • Value at Risk (VaR)