We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stoc...We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method. Key words ruin probability - variable premium rate - diffusion process - Markov intensity CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)展开更多
In order to examine the effect of spatial scale and building exposure distribution on the pure rate of earthquake catastrophe insurance,this study described three modules for rate determination,put forward the general...In order to examine the effect of spatial scale and building exposure distribution on the pure rate of earthquake catastrophe insurance,this study described three modules for rate determination,put forward the general assumptions and principles for calculating the pure insurance rate,and introduced three types of building distribution and their calculation.Taking Tangshan City of Hebei Province in China as an example,we analyzed the pure rate of regional earthquake insurance in terms of spatial scale and building exposure distribution by using the method of control variables.The results show that for districts(or counties)with large differences in seismic risk,the risk areas can be further divided to apply differential rates.In areas with a diverse distribution of potential earthquake source areas and large differences in building density,there is a risk of overestimating or underestimating the pure rate of earthquake insurance when buildings are distributed evenly or partially evenly.This violates the break-even principle of rate setting.This study also provides a reference for earthquake catastrophe insurance companies to choose the spatial scale and the detailed level of exposure distribution in rate determination.展开更多
文摘We consider a risk model with a premium rate which varies with the level of free reserves. In this model, the occurrence of claims is described by a Cox process with Markov intensity process, and the influence of stochastic factors is considered by adding a diffusion process. The integro-differential equation for the ruin probability is derived by a infinitesimal method. Key words ruin probability - variable premium rate - diffusion process - Markov intensity CLC number O 211.9 Foundation item: Supported by the National Natural Science Foundation of China (10071058, 70273029)
基金funded by the National Key Research and Development Program(2022YFC3003500)the 111 Project(D21001).
文摘In order to examine the effect of spatial scale and building exposure distribution on the pure rate of earthquake catastrophe insurance,this study described three modules for rate determination,put forward the general assumptions and principles for calculating the pure insurance rate,and introduced three types of building distribution and their calculation.Taking Tangshan City of Hebei Province in China as an example,we analyzed the pure rate of regional earthquake insurance in terms of spatial scale and building exposure distribution by using the method of control variables.The results show that for districts(or counties)with large differences in seismic risk,the risk areas can be further divided to apply differential rates.In areas with a diverse distribution of potential earthquake source areas and large differences in building density,there is a risk of overestimating or underestimating the pure rate of earthquake insurance when buildings are distributed evenly or partially evenly.This violates the break-even principle of rate setting.This study also provides a reference for earthquake catastrophe insurance companies to choose the spatial scale and the detailed level of exposure distribution in rate determination.
