Abstract: The aim of this paper is to present changes in the distribution of insurance premiums in Bosnia and Herzegovina (BiH) for the period from 2010 to 2024. The research results relate to determining the form and intensity of competition in life and non-life insurance. Six concentration measures and the Lorenz curve describe different levels of competition in the non-life and life insurance markets in BiH. The results 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 non-life insurance premiums are statistically significant for almost all of the examined inequality measures. The concentration ratio C5, the Herfindahl-Hirschman index (HHI), the Gini coefficient (G), and the 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 indices is expected, with the exception of entropy, which is expected to decline slightly, indicating a reduction in the number of companies. The movement of gross life insurance premiums is shaped by concentration measures whose trend models do not display the same monotonicity. In the period after 2025, the models forecast a decrease in entropy, RI, G, and HHI, while the models for the concentration ratio C5 and HTI forecast a slight increase in these indices. Together with the simultaneous growth of the total premium, this can be interpreted as the beginning of a concentration process in the insurance market.

Keywords: Gross premium; entropy; Hall-Tideman; Herfindahl-Hirschman; trend forecasting; Rosenbluth