The Hungarian economy exhibits a notable underinsurance phenomenon, with insurance penetration at a mere 2.8%, significantly lower than the European Union average of 8%. This situation indicates substantial growth potential within the Hungarian insurance market, particularly in the life and non-life insurance sectors, contingent upon the development of solvent demand and favorable demand-stimulating factors. Anticipated transformations in the structure of the Hungarian insurance market may arise due to both endogenous and exogenous influences, likely resulting in heightened market concentration and alterations in competitive dynamics. This study aims to conduct an analysis of the historical and expected future transformations of the Hungarian insurance market structure by utilizing publicly available data on gross premium income. The analysis employs traditional market structure indicators, such as market shares, concentration ratios, and the Herfindahl-Hirschman Index (HHI), while also examining market share transitions through the application of the Markov chain method. Markov transition probabilities offer a more accurate representation of historical market structure processes compared to conventional market structure indicators. Furthermore, the calculation of these transition probabilities facilitates the prediction of anticipated future changes in market shares. The stationary (ergodic) distribution of market shares, derived from the transition probability matrix, denotes a market share distribution toward which the market converges under stable conditions. This approach also enables the computation of an equilibrium market share distribution achievable in the future under specified conditions, driven by the internal mechanisms of the market. The analysis reveals an upward trend in the market shares of larger companies and an increase in market concentration across both the life and non-life insurance sectors in Hungary. Traditional methods of indirect measurement indicate a prospective rise in market concentration and a potential decline in competitive conditions. However, when considering stationarity, the invariant distributions estimated via the Markov chain methodology suggest a decrease in the market shares of the largest companies, accompanied by a leveling effect among leading firms. This indicates that, assuming unchanged conditions over the past decade, the intrinsic processes of the market could lead to a less concentrated market structure in both the life and non-life insurance sectors of the Hungarian insurance market. Removing the stationarity assumption presents new opportunities for determining the equilibrium state of the insurance market under specific conditions. Future research will venture further in this direction. The objective is to develop a model capable of indirectly measuring market power, which will provide essential insights for competition authorities and management of market participants, even within asymmetric information contexts, regarding the anticipated trajectory of market structure transformation.