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Optimal premium pricing in a competitive stochastic insurance market with incomplete information: A Bayesian game-theoretic approach

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  • Mourdoukoutas, Fotios
  • Boonen, Tim J.
  • Koo, Bonsoo
  • Pantelous, Athanasios A.

Abstract

This paper examines a stochastic one-period insurance market with incomplete information. The aggregate amount of claims follows a compound Poisson distribution. Insurers are assumed to be exponential utility maximizers, with their degree of risk aversion forming their private information. A premium strategy is defined as a mapping between risk-aversion types and premium rates. The optimal premium strategies are denoted by the pure-strategy Bayesian Nash equilibrium, whose existence and uniqueness are demonstrated under specific conditions on the insurer-specific demand functions. Boundary and monotonicity properties for equilibrium premium strategies are derived.

Suggested Citation

  • Mourdoukoutas, Fotios & Boonen, Tim J. & Koo, Bonsoo & Pantelous, Athanasios A., 2024. "Optimal premium pricing in a competitive stochastic insurance market with incomplete information: A Bayesian game-theoretic approach," Insurance: Mathematics and Economics, Elsevier, vol. 119(C), pages 32-47.
    • Handle: RePEc:eee:insuma:v:119:y:2024:i:c:p:32-47
    DOI: 10.1016/j.insmatheco.2024.07.006
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    More about this item

    Keywords

    Competitive insurance markets; Incomplete information; Bayesian Nash equilibrium; Combined ratio;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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