Research On The Economic Capital Allocation Of Insurance Companies' Dependent Risks

Economic capital measures the unintended loss of insurers,it is possible to solve the problem of solvency of the insurance company by allocating the economic capital to the individual risk(or loss).It can also effectively measure the performance and improve the capital use efficiency of the insurance company.This article mainly studies the risk allocation of economic capital.This problem mainly includes three elements: one is the measure of risk;the second is the measure of dependency;the third is the economic capital allocation method.First of all,we need to determine the total economic capital,and the economic capital measurement needs to use the risk measure.Economic capital measures unintended losses,from the definition of economic capital,we need to select the appropriate risk measure to measure economic capital.This article chooses the TVaR risk measure,because TVaR not only satisfies the consistency axiom,but also measures the risk of the tail of the loss,while the insurance company’s loss(or compensation)tends to have thick tail characteristics.Second,the significance of economic capital allocation is to optimize the amount and structure of economic capital.And the interdependence between risks has an impact on the quantity and structure of economic capital.On the one hand,if the interdependence between risks is not taken into account,the economic capital allocated to a single risk can not match the risk,that is,there is an unreasonable capital structure;On the other hand,when there is a positive correlation between the different risks,the total amount of economic capital required will be greater than the independent situation;When there is a negative dependency,the total amount of economic capital required is less than the independent situation due to the risk diversification effect.When there is a negative dependency,the total amount of economic capital required is less than the independent situation due to the risk diversification effect.Copula can measure the non-linear,asymmetric dependent structure of insurance company risk,the correlation coefficient can not.Therefore,this article chooses the FGM Copula to construct the interdependent structure of risk.For the economic capital allocation method,the Tail Mean-Variance model(TMV)is an optimized capital allocation method with the aim of minimizing the loss and can simultaneously measure the variability of the tail risk and loss function of the loss.Therefore,this article uses TMV model to configure economic capital.This article base on the TMV model,use FGM Copula to construct the interdependence of risk,and then the analytic solution of the model is deduced under the assumption that the single risk(or loss)obeys the exponential distribution.In this artical,numerical simulation is used to simulate the results of economic capital allocation,and the influence of dependency on economic capital allocation is analyzed by numerical simulation.According to the simulation results,it can be observed that the impact of dependency on economic capital allocation is reflected in two aspects.First,the dependence on the total economic capital has a certain impact,when there is a positive dependency,the total economic capital is greater than the total economic capital under the circumstances;when there is a negative dependency,due to risk diversification effect,The total economic capital is smaller than in the case of independence.Secondly,with the change of dependency parameters,the proportion of economic capital with single risk allocation is also changing and showing certain regularity.