Abstarct: The main purpose of this study is to present the application of the generalized Lorenz curve and the Gini coefficient in risk management of insurance portfolios, fair pricing of insurance policies and the selection of an appropriate pricing model. In this research, the insurance data of the DAY-Insurance Company in the field of insurance supplemental treatment activity was used to validate the research, and in line with its objectives, the insurance data was statistically analyzed in the R software environment. The analysis of the insurance risk of the insurance company in the field of insurance activity completion of treatment in relation to the characteristics of the insured (such as gender, age, place of residence) shows that these factors play a decisive role in the level of insurance risk of the insurance company. For fair treatment completion insurance pricing, multiple pricing models are estimated baxsed on the characteristics of the insured and the appropriate model is selected baxsed on the ABC criterion (the area enclosed between the CC and LC curves). The results show that the influence of all insurance factors on the characteristics of the insured is significant for the selected pricing model; The influence of gender on the insurer's risk is greater than the influence of the insured's age; While the effect of the place of residence factor is larger than the effect of age and sex factors in some provinces.baxsed on this, it can be concluded that the implementation of price discrimination measures (gender, age and province) is necessary to reduce the insurance risk of insurance companies.