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.

market share; market concentration; competition; markov chains; insurance; equilibrium; ergodic distribution

Bikker, J. A., Haaf, K. (2002): Measures of competition and concentration in the banking industry: a review of the literature. Economic & Financial Modelling, 9(2), 53-98.

Bikker, J. A., Leuvensteijn, M. V. (2005): An exploration into competition and efficiency in the Dutch life insurance industry. CPB Discussion Paper, No 48, http://www.dnb.nl/binaries/Working%20Paper%2047_tcm46-146704.pdf

Bundeskartellamt (2012): Guidance on Substantive Merger Control, https://www.bundeskartellamt.de

Cabral, L. M. B. (2000): Introduction to Industrial Organization. MIT Press.

Clayton Act (1914) https://www.law.cornell.edu/wex/clayton_antitrust_act

Competition Act (1998)

Code de commerce: TITRE III (2024): De la concentration économique. (Articles L430-1 à L430-10)

Cummins, J. D. (2001): Statistical and Financial Models of Insurance Pricing and the Insurance Firm. The Journal of Risk and Insurance, Vol. 58, No. 2. 261-302. p.

Cummins, J. D., Weiss M. A. (2000): ‘Analysing firm performance in the insurance industry using frontier efficiency and productivity methods’. in: Handbook of Insurance, ed. by Georges Dionne, Kluwer, Massachussetts.

Demsetz, H (1982): Barriers to Entry. American Economic Review, Vol. 72. No. 1., 47-57 p.

Denny, M. (1980): Measuring the Real Output of the Life Insurance Industry: A Comment. The Review of Economics and Statistics, Vol. 62, No. 1., 150-152. p.

Enterprise Act (2002)

European Commission (2004): Guidelines on the assessment of horizontal mergers under the Council Regulation on the control of concentrations between undertakings (2004/C 31/03).

Fenn, P., Vencappa, D., Diacon, S., Klumpes, P., O’Brien, Ch. (2004): Market Structure and the Efficiency of European Insurance Companies: a Stochastic Frontier Analysis, letöltés helye: http://neumann.hec.ca/gestiondesrisques/dim/Papers/Fenn-Vencappa-Diacon-Klumpes-OBrien.pdf

Hall, M., Tideman, N. (1967): Measures of Concentration. Journal of the American Statistical Association, 62(317), 162-168.

Hirschhorn, R., Geehan, R. (1977): Measuring the real output of the life insurance industry. Review of Economics and Statistics, Vol. 59., No. 2., 211-219. p.

Jaehyung, A., Mikhaylov, A., Sang-uk, J. (2020): The Strategy of South Korea in the Global Oil Market. Energies, 13(10), 2491. https://doi.org/10.3390/en13102491

Klugman, S., Panjer, H., Willmot, G. (2012): Loss Models: From Data to Decisions (4th ed.). Wiley.

Kovács, N. (2014). A piaci erő közvetett mérése a biztosítási piacon, IDResearch Kft.; Publikon Kiadó

Kwoka, J. E., White, L. J. (2004): The Antitrust Revolution: Economics, Competition, and Policy. Oxford University Press.

Marker, J.O. (1998): Studying policy retention using Markov chains. Casualty Actuarial Society.

Motta, M. (2004): Competition Policy. Theory and practice. Cambridge University Press, New York

Norberg, R. (2002): Anomalous PDEs in Markov chains: domains of validity and numerical solutions. Research Report, London School of Economics.

Pantelous, A. & Passalidou, E. (2015): Optimal premium strategies for competitive general insurance markets. Applied Mathematics and Computation.

Pindyck, R. S., Rubinfeld, D. L. (2013). Microeconomics. Pearson.

Rhoades, S. A. (1993): The Herfindahl-Hirschman Index. Federal Reserve Bulletin, 79, 188-189.

Scherer, F. M., Ross, D. (1990): Industrial Market Structure and Economic Performance. Houghton Mifflin.

Schmalensee, R. (1977): Using H-index of concentration with published data. Review of Economics and Statistics, Vol. 59., No.2., 186-193. p.

Schmalensee, R., Willig R. (1989): Handbook of Industrial Organization. Elsevier, North Holland

Sherman Act (1890) https://www.archives.gov/milestone-documents/sherman-anti-trust-act

Slade, M.E. (1986): Exogenity test of Market Boundaries Applied to Petroleum Products. Journal of Industrial Economics, Vol. 34., No.3., 291-303. p.

Stepanova, D., Yousif, N. B. A. - Karlibaeva, R. - Mikhaylov A. (2024): Current analysis of cryptocurrency mining industry. Journal of Infrastructure, Policy and Development, 8(7), 4803. https://doi.org/10.24294/jipd.v8i7.4803

Stigler, G.J., Sherwin, R.A. (1985): The Extent of the Market. Journal of Law and Economics, Vol. 28., No. 3., 555-585. p.

Stokey, N. L., Lucas E.R., Prescott, E.C. (1989): Recursive Methods in Economic Dynamics, Harvard University Press, http://books.google.hu/books?id=tWYo0QolyLAC&dq=Recursive+methods+in+economic+dynamics&printsec=frontcover&source=bn&hl=hu&ei=sRnsS-C4K4KbONnwtdcH&sa=X&oi=book_result&ct=result&resnum=4&ved=0CCwQ6AEwAw#v=onepage&q&f=false

Sydsaeter, K., Hammond, P.I. (2006): Matematika közgazdászoknak. Aula Kiadó, Budapest

Tirole, J. (1988): The Theory of Industrial Organization. MIT Press.

U.S. Department of Justice and Federal Trade Commission (2010). Horizontal Merger Guidelines, https://www.justice.gov/atr/horizontal-merger-guidelines-08192010

UK Competition and Markets Authority (CMA) (2021) https://assets.publishing.service.gov.uk/media/61f952dd8fa8f5388690df76/MAGs_for_publication_2021_--_.pdf

Wu, H. (2017): Potential games with aggregation in non-cooperative general insurance markets. ASTIN Bulletin. This paper integrates Markov chain theory with insurance market analysis, examining the long-term dynamics of firm rankings and stability in competitive markets.