Chinese Earthquake Insurance Fund Calculates

China is a country prone to seismic disasters,which cause huge losses to the people and the government every year.China relies heavily on state subsidies to pay out compensation for earthquakes,with insurance coverage of less than 10%of earthquake losses,far below the international insurance market rate of around40% for natural disasters.This has resulted in the state treasury bearing most of the losses in the event of an earthquake catastrophe,seriously affecting the normal operation of the state treasury.Therefore,there is an urgent need to establish and improve the earthquake catastrophe insurance fund system in China,to study the risk measurement theory,and to prepare sufficient insurance funds to cope with the losses caused by various earthquake disasters through scientific risk measurement.The core technology for the establishment of a catastrophe insurance fund system is the modelling and analysis of earthquake loss data.The small amount of seismic loss data,especially for extreme seismic hazards,the spikes and tails,and the small samples,pose a great challenge to the modelling of seismic loss data.In this paper,we study the modelling of earthquake loss distribution from the theoretical and practical needs of fitting earthquake loss distribution for earthquake insurance fund estimation.This paper takes earthquakes with direct economic losses of one million yuan or more that occurred in China from 1990 to 2020 as the object of study,and focuses on how to improve the modelling of the tail data from both parametric and non-parametric approaches.In terms of parametric distribution modeling,this paper proposes to use the modified Champernowne distribution to fit the distribution of earthquake losses and compare it with the three generalized extreme value distributions of Fréchet,Weibull and Gumbel and the mixture of combined Weibull-GPD distribution widely used in existing studies.The results show that the Champernowne distribution fits better.In terms of non-parametric modeling,this paper proposes an improved adaptive kernel density estimation and an adaptive combined kernel density estimation,and compares them with the traditional Gaussian kernel density estimation,using the mean error score(MAPE)and the root mean square error(RMSE)to compare the three non-parametric kernel density estimation methods in terms of the overall and tail fitting effects,respectively.The results show that the adaptive combined kernel density estimation provides the best fit.Finally,based on the fitting of the distribution of earthquake losses,this paper measures the earthquake insurance fund based on the risk measure of Va R,which provides a theoretical reference for the establishment of an earthquake insurance fund system in China.The Champernowne distribution and the self-adaptive kernel density estimation proposed in this paper are better than the existing models in fitting the cusp-thick-tailed catastrophe loss data,which provides a new idea for the measurement of earthquake insurance fund in China,and also for the measurement of insurance fund for other natural disasters.