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Bowley vs. Pareto optima in reinsurance contracting

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  • Boonen, Tim J.
  • Ghossoub, Mario

Abstract

The notion of a Bowley optimum has gained recent popularity as an equilibrium concept in problems of risk sharing and optimal reinsurance. In this paper, we examine the relationship between Bowley optimality and Pareto efficiency in a problem of optimal reinsurance, under fairly general preferences. Specifically, we show that Bowley-optimal contracts are indeed Pareto efficient but they make the insurer indifferent with the status quo (hence providing a partial first welfare theorem). Moreover, we show that only those Pareto-efficient contracts that make the insurer indifferent between suffering the loss and entering into the reinsurance contract are Bowley optimal (hence providing a partial second welfare theorem). We interpret these result as indicative of the limitations of Bowley optimality as an equilibrium concept in this literature. We also discuss relationships with competitive equilibria, and we provide illustrative examples.

Suggested Citation

  • Boonen, Tim J. & Ghossoub, Mario, 2023. "Bowley vs. Pareto optima in reinsurance contracting," European Journal of Operational Research, Elsevier, vol. 307(1), pages 382-391.
    • Handle: RePEc:eee:ejores:v:307:y:2023:i:1:p:382-391
    DOI: 10.1016/j.ejor.2022.08.003
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    References listed on IDEAS

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    3. David Landriault & Fangda Liu & Ziyue Shi, 2024. "Performance-based variable premium scheme and reinsurance design," Papers 2412.01704, arXiv.org.
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    5. Cao, Jingyi & Li, Dongchen & Young, Virginia R. & Zou, Bin, 2023. "Reinsurance games with two reinsurers: Tree versus chain," European Journal of Operational Research, Elsevier, vol. 310(2), pages 928-941.
    6. Zhang, Caibin & Liang, Zhibin & Yuan, Yu, 2024. "Stochastic differential investment and reinsurance game between an insurer and a reinsurer under thinning dependence structure," European Journal of Operational Research, Elsevier, vol. 315(1), pages 213-227.

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    More about this item

    Keywords

    Risk management; Optimal reinsurance; Pareto optimality; Bowley optimality; Convex risk measures;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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