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Bertrand oligopoly in insurance markets with Value at Risk Constraints

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  • Kolos Csaba 'Agoston
  • Veronika Varga

Abstract

Since 2016 the operation of insurance companies in the European Union is regulated by the Solvency II directive. According to the EU directive the capital requirement should be calculated as a 99.5\% of Value at Risk. In this study, we examine the impact of this capital requirement constraint on equilibrium premiums and capitals. We discuss the case of the oligopoly insurance market using Bertrand's model, assuming profit maximizing insurance companies facing Value at Risk constraints. First we analyze companies' decision on premium level. The companies strategic behavior can result positive as well as negative expected profit for companies. The desired situation where competition eliminate positive profit and lead the market to zero-profit state is rare. Later we examine ex post and ax ante capital adjustments. Capital adjustment does not rule out market anomalies, although somehow changes them. Possibility of capital adjustment can lead the market to a situation where all of the companies suffer loss. Allowing capital adjustment results monopolistic premium level or market failure with positive probabilities.

Suggested Citation

  • Kolos Csaba 'Agoston & Veronika Varga, 2024. "Bertrand oligopoly in insurance markets with Value at Risk Constraints," Papers 2404.17915, arXiv.org.
    • Handle: RePEc:arx:papers:2404.17915
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    References listed on IDEAS

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    1. René Doff, 2016. "The Final Solvency II Framework: Will It Be Effective?," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan;The Geneva Association, vol. 41(4), pages 587-607, October.
    2. MOSSIN, Jan, 1968. "Aspects of rational insurance purchasing," LIDAM Reprints CORE 23, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Michael Rothschild & Joseph Stiglitz, 1976. "Equilibrium in Competitive Insurance Markets: An Essay on the Economics of Imperfect Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 629-649.
    4. D'Arcy, Stephen P & Doherty, Neil A, 1990. "Adverse Selection, Private Information, and Lowballing in Insurance Markets," The Journal of Business, University of Chicago Press, vol. 63(2), pages 145-164, April.
    5. Bi, Junna & Cai, Jun, 2019. "Optimal investment–reinsurance strategies with state dependent risk aversion and VaR constraints in correlated markets," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 1-14.
    6. Wambach, Achim, 1999. "Bertrand competition under cost uncertainty," International Journal of Industrial Organization, Elsevier, vol. 17(7), pages 941-951, October.
    7. Kliger, Doron & Levikson, Benny, 1998. "Pricing insurance contracts -- an economic viewpoint," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 243-249, July.
    8. Hao, MingJie & Macdonald, Angus S. & Tapadar, Pradip & Thomas, R. Guy, 2018. "Insurance loss coverage and demand elasticities," Insurance: Mathematics and Economics, Elsevier, vol. 79(C), pages 15-25.
    9. Roy Kouwenberg, 2018. "Strategic asset allocation for insurers under Solvency II," Journal of Asset Management, Palgrave Macmillan, vol. 19(7), pages 447-459, December.
    10. Marcos Escobar & Paul Kriebel & Markus Wahl & Rudi Zagst, 2019. "Portfolio optimization under Solvency II," Annals of Operations Research, Springer, vol. 281(1), pages 193-227, October.
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