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Pareto-optimal reinsurance under Vajda condition and heterogenous beliefs

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  • Fengzhu Chang
  • Ying Fang

Abstract

This article revisits the Pareto-optimal reinsurance problem under the Value at Risk (VaR) risk measure. To encapsulate the essence of reinsurance and mitigate moral hazard, we assume that the ceded loss function adheres to the Vajda condition and incentive compatibility condition. Given that the insurer and reinsurer hold diverse probability beliefs regarding potential risk losses, the article explores reinsurance design under arbitrary belief heterogeneity. Subsequently, we concentrate on belief heterogeneity that satisfies the monotone hazard rate (MHR) condition. Against this backdrop, we formulate a Pareto-optimal reinsurance model. Initially, we derive the explicit expression for optimal reinsurance without risk constraints by leveraging the relationship between the marginal indemnification function (MIF) and the ceded loss function. Subsequently, we derive the explicit expression for optimal reinsurance with risk constraints. Last, we present a numerical study to assess the impact of the weighting factors on Pareto-optimal reinsurance.

Suggested Citation

  • Fengzhu Chang & Ying Fang, 2025. "Pareto-optimal reinsurance under Vajda condition and heterogenous beliefs," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(24), pages 7890-7917, December.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:24:p:7890-7917
    DOI: 10.1080/03610926.2025.2485340
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