کاربردهای منحنی لورنز و ضریب جینی تعمیم‌یافته در بیمه

Objective: The Lorenz curve and the Gini coefficient were first proposed as tools to measure inequality in the wealth distribution. The increasing application of these tools and their generalized versions in various sciences has led to numerous studies of the Lorenz curve and its applications. The main objective of this research is to present and localize the applications of the generalized Lorenz curve and the Gini coefficient in the insurance industry for management of insurance portfolio risk, ranking of insurance risk factors, fair pricing of insurance policies, and selection of appropriate insurance policy pricing models.

Methods: Available compensation and insurance premium data related to Bimah-DAY's supplementary health insurance contracts, with contract start dates ranging from January 21, 2018, to May 12, 2018, were used to validate the study. Insurance risk analysis was performed based on the characteristics of the insured by comparing the relativity index (the ratio of claims paid to premiums received) of the insurance portfolio. The relative importance of the factors for the level of compensation for the insured person was determined by calculating the concentration coefficient and plotting the Lorenz curves and the corresponding concentration curves; Several pricing models based on insured features were estimated using the generalized least squares (GLM) method. The appropriate model was then selected using the ABC criterion (area enclosed between the Lorenz curve and the concentration curve).

Results: The results showed that the relativity index of insurance portfolios is not the same depending on the characteristics of the insured (such as gender, age, province of residence). The insurance company's insurance loss from the insurance coverage of 371,403 people in the treatment completion insurance contracts amounted to more than 127 billion riyals in the reporting period. A bout 28 percent of the damage amount is attributed to the male gender (men) and the remaining 72 percent to the female gender (women group). An insurance portfolio consisting of age groups from 0 to 21 years was profitable for the insurance company, but for people over 68 years of age it was a loss.

In five provinces of the country (Qom, Hormozgan, East Azerbaijan, Razavi-Khorasan and Kurdistan) the ratio was below one and in other provinces it was above one. The insurance company's loss by each insured person in Gilan Province is higher than other provinces, with a ratio of 3.046. The dependence of the compensation paid on the level of coverage of the insurance contracts is stronger than on the characteristics of the insured person. The gender and place of residence of the insured person had an inconsistent impact on the compensation paid and the insurance risk. In the selected pricing model, the effect of all characteristics of the insured was significant; The influence of age on the insurance company's risk was greater than the influence of the gender of the insured; While the influence of province of residence was greater than the influence of age and gender in some provinces.

Conclusion: Due to the significance of the coefficient of all three factors of gender, age and place of residence in the chosen pricing model and the non-uniformity of the index of relativity of insurance portfolios according to the characteristics of the insured, we came to the conclusion that in order to reduce the losses of the insurance company in the field of supplementary treatment insurance, the application price discrimination policies based on age, gender, etc. required.