Estimation of the Catastrophic Risk using Mixture Models

Abstract

Indonesia is one of the countries in the world that is susceptible to various types of natural disasters such as earthquakes, floods, etc. These events do not occur very often, however, they cause massive financial loss. This risk of loss is termed as a catastrophic risk where it not only affects the individual but also the government and at the same time posing a threat to insurance companies if they do not have sufficient resources to make a payment of claims. However, due to the complexity and uncertainty of natural hazards, measuring this risk is quite challenging. This paper proposes an estimation method of the catastrophic risk based on Value-at-Risk (VaR) of total loss from natural disasters in Indonesia. A key issue for estimating VaR is to fit an appropriate distribution. Extreme value distribution, such as Generalized Pareto Distribution (GPD) has been used to assess the tail behavior of extreme loss. However, this distribution does not give any information about the central behavior that may affect the estimation of the model parameter in GPD. Therefore, this paper utilized mixture models that combine the parametric form of loss distributions such as gamma, Weibull, and lognormal distribution with GPD. The result shows that VaR estimations are quite different under different mixture models and confidence levels. In addition, the lognormal-GPD model is selected as the best model that fits data best with the highest value of Log-likelihood