Pricing Analysis Of Motor Vehicle Insurance Optimal Deductible

The motor vehicle insurance business of most China’s property insurance companies have been faced with problems such as high payment rate, high operating costs and low profitability during the past several years. The new round of commercial auto insurance rates reform undoubtedly have brought new challenges to the insurance companies. Compared to the absolute franchise system, which are used more in China’s motor vehicle insurance market, ordinary deductible has more advantages in certain aspects such as avoiding inefficient high frequency of payments for small sums of claims and reducing moral hazard. Thus it would be an effective method that the property insurance companies use more ordinary deductible to substitute absolute franchise system to reduce the frequency of payments for small sums of claims, which will reduce the expenditure and improve the management efficiency and profitability.After introducing basic theories of deductible and the application present situation in China’s motor vehicle insurance market, this paper draw lessons from the research results of scholars at home and abroad, and makes some assumptions, based on which this paper establishes an pricing model for the optimal deductible. The model is a mathematical model which maximizes the profit of insurance companies, and the restriction is that the person’s utility is increased after purchasing insurance. And the model aims at finding a feasible and practical method for the pricing of optimal deductible. The model’s initial solution results show that the optimal deductible is positively related to the probability of loss and the cost of claims. That is to say, the insurers can enjoy lower deductible to get a more comprehensive protection as long as the insurers drive carefully to reduce the accident probability and insurance companies improve business efficiency to reduce the costs of the claim.To increase the practicability of the pricing model, this paper uses the relevant data of G property insurance company to estimate the parameters in the model and then solve the optimal deductible of G insurance company. Due to some of the assumptions are unreasonable, the empirical result is much higher than the reality level. Later, this paper discusses the reasons why the empirical result is higher than the reality level. The several reasons are the loss distribution has a heavy tail which leads to a lower estimation value for parameter λ, the selection of risk aversion coefficient is unreasonable and the sample is too small and so on. The discussion may provide the direction of improvement for the model been used to pricing motor vehicle insurance optimal deductible in reality.