Summary: This paper aims to present changes in the distribution of insurance premiums in Bosnia and Herzegovina (BiH) from 2010 to 2024. The research focuses on determining the form and intensity of competition in life and non-life insurance. Six concentration measures and the Lorenz curve are used to describe varying levels of competition in the non-life and life insurance markets in BiH. The findings indicate a high level of competition in non-life insurance and weak to moderate competition in life insurance. Quadratic trend models for the concentration indices of gross premiums in non-life insurance are statistically significant for almost all the examined inequality measures. The concentration ratio C5, Herfindahl-Hirschman index (HHI), Gini coefficient (G), and Rosenbluth index (RI) are described by a quadratic trend model with a positive leading coefficient, while entropy follows a second-degree polynomial trend model with a negative leading coefficient. This suggests that over the next five to ten years, a slight increase in the concentration index is expected, except for entropy, which is projected to decrease slightly, indicating a reduction in the number of companies. The movement of gross life insurance premiums is influenced by concentration measures whose trend models do not display the same monotonicity. After 2025, the models forecast a decrease in entropy, RI, G, and HHI, while the models for the concentration ratio C5 and HTI predict a slight increase in these indices. This, together with the simultaneous growth of the total premium, may be interpreted as the beginning of the concentration process in the insurance market.