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Bowley-optimal convex-loaded premium principles

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  • Ghossoub, Mario
  • Li, Bin
  • Shi, Benxuan

Abstract

This paper contributes to the literature on Stackelberg equilibria (Bowley optima) in monopolistic centralized sequential-move insurance markets in several ways. We consider a class of premium principles defined as expectations of increasing and convex functions of the indemnities. We refer to these as convex-loaded premium principles. Our analysis restricts the ex ante admissible class of indemnity functions to the two most popular and practically relevant classes: the deductible indemnities and the proportional indemnities, both of which satisfy the so-called no-sabotage condition. We study Bowley optimality of premium principles within the class of convex-loaded premium principles, when the indemnity functions are either of the deductible type or of the coinsurance type. Assuming that the policyholder is a risk-averse expected-utility maximizer, while the insurer is a risk-neutral expected-profit maximizer, we find that the expected-value premium principle is Bowley optimal for proportional indemnities, while the stop-loss premium principle is Bowley optimal for deductible indemnities under a mild condition. Methodologically, we introduce a novel dual approach to characterize Bowley optima.

Suggested Citation

  • Ghossoub, Mario & Li, Bin & Shi, Benxuan, 2025. "Bowley-optimal convex-loaded premium principles," Insurance: Mathematics and Economics, Elsevier, vol. 121(C), pages 157-180.
    • Handle: RePEc:eee:insuma:v:121:y:2025:i:c:p:157-180
    DOI: 10.1016/j.insmatheco.2025.01.006
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    More about this item

    Keywords

    Optimal premium principles; Expected-value premium principle; Stop-loss premium principle; Stackelberg equilibrium; Bowley optima; Dual approach;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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