Research On The Design Of Optimal Earthquake Index Insurance Policies

In recent years is a period of frequent severe earthquakes,which causes a gradually increasing of economic losses due to earthquakes all over the world and an increasing demand of earthquake risk management.As a crucial component in the comprehensive earthquake risk management system and the major financial way to diversify the earthquake risk through the insurance markets,earthquake insurances play important roles in supporting the liquidity of funds aiming to rebuild the suffering areas.As early as 1920,earthquake insurance was sold as an option of the fire loss insurance for houses in Japan,which firstly acknowledged the positive effect of earthquake insurance in earthquake risk management.As a new type of earthquake insurance products representing the innovation of designing principle for earthquake insurance products,the index-based earthquake insurance does not only help to facilitate the development of earthquake business lines and markets,but also provide valuable experience for transferring and diversifying other types of uninsurable risks to the insurance markets.This thesis classifies index-based earthquake insurance products into two categories based on whether the indemnity depends on the actual losses directly: the first is insurance products with indemnities completely depending on the index(EQI for short);the other is insurance products with indemnities partially depending on the index(EQII for short).By combining the Expected Utility Theory,Decomposition of Catastrophe Risks,and the shared properties of both index-based earthquake insurance products,this thesis proposes a general framework for designing the indemnity of index-based earthquake insurance products and obtains the necessary condition for the Pareto optimal risk sharing between the insureds and insurers using the stochastic control theory.Based on this condition,this thesis deduces the explicit solution for the Pareto optimal indemnity design under the assumption of CARA utilities for both insureds and insurers.Moreover,this thesis calculates the Pareto optimal indemnity designs as well as the actuarial net premium for both EQI and EQII with magnitude and intensity as the indices respectively using the empirical analysis involving earthquake loss data of Chinese mainland from 1990 to 2017 and the nonparametric regression with measurement errors.Hence this thesis illustrates the complete procedure of designing and pricing the Pareto optimal index-based earthquake insurance products under the proposed general framework.The resulting EQII products share similar pattern with the existing EQII products.Besides designing the indemnity using economical methods given the earthquake index,this thesis proposes the basic principles to construct earthquake indices by analyzing the characteristics and properties of earthquake parameters.Currently popular earthquake parameters include the magnitude and intensity of the epicenter,where magnitude represents the total energy released by earthquakes and thus has only one record for each earthquake while the intensity itself is a measure of damage to the surface and hence could be describes by the isoseismal map due to the geographic information.Thus,this thesis tends to choose intensity as the index for designing insurance products.However,it is insufficient to reduce the basis risk by using the intensity of the epicenter as the index directly.Therefore,this thesis suggests to construct parametric index for designing earthquake insurance products by the isoseismal map based on the intensity.In addition,this thesis also examines the multiple claims during the term of the indexbased earthquake insurance policies.Unlike the earthquake catastrophe financial derivatives,the index-based earthquake insurance focuses on the settlements of claims as an insurance product having higher requirement on protection against losses caused by earthquakes.In areas with high earthquake frequencies,the uncertainties of the time and location of the earthquakes are crucial obstacles for reasonable pricing of the indexbased insurance.Hence this thesis considers extra triggering conditions to define the coverage of the index-based earthquake insurance such that the probability of more than two claims during the term is as small as possible.As experiences and data accumulated,the extra triggering conditions could be gradually weakened such that a reasonable coverage of index-based earthquake insurance could be eventually obtained by continueing to adjust these conditions.By the aforementioned studies,this thesis concludes the following by analysis:(1)From the aspect of risk sharing,the necessary condition for the claim as the function of the earthquake index to be Pareto optimal is derived using the optimal control theory.The explicit form of such a function is obtained under the constant absolute risk aversion(CARA)assumption.The result shows that the Pareto optimal claim amount of the index-based earthquake insurance should be a nonlinear function of earthquake index depending on the corresponding earthquake catastrophe risk decomposition,where a deductible minimizing the basis risk is involved;while the Pareto optimal covered percentage of losses should be a hyperbolic function or a constant function of earthquake index for the index-based earthquake coinsurance.Moreover,the result also indicates that the insurers with limited risk management capacity might take part in the index-based earthquake insurance market by suitable indemnity design so that they could benefit from running the business of index-based earthquake insurance,while diversify the earthquake risk further.In addition,the results suggest that to reflect the regional differences in the policy design of index-based earthquake insurance it is not only necessary to provide various options of premium rates but also provide different claim amount design according to these regional differences.(2)From the aspect of earthquake index selection,this thesis compares the feasibility to be the earthquake index of two major parameters: magnitude and intensity and prefers the earthquake intensity as a more reasonable choice for the earthquake index.Moreover,this thesis also analyzes three types of indices: the industrial loss index,pure parametric index and parametric index and finds out that the parametric indices could most efficiently balance the transparency of information and basis risk and hence proposes to calculate the weighted average of intensity as the parametric index involving the geographical information of the loss with the weights taken according to the intensity segmentation of the isoseismal map.(3)From the aspect to avoiding multiple claims,this thesis proposes to add claim triggerting condition to control the probability of occurrence of more than one claims in order to improve the sustainability of the index-based earthquake insurance at the initial stage;as the data is accumulated and the law of the earthquake losses is better understood,the index-based earthquake insurance policy design could be improved by adjusting the claim triggering condition to accept multiple claims as long as the solvency allows.