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Multi-constrained optimal reinsurance model from the duality perspectives

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  • Cheung, Ka Chun
  • He, Wanting
  • Wang, He

Abstract

In the presence of multiple constraints such as the risk tolerance constraint and the budget constraint, many extensively studied (Pareto-)optimal reinsurance problems based on general distortion risk measures become technically challenging and have only been solved using ad hoc methods for certain special cases. In this paper, we extend the method developed in Lo (2017a) by proposing a generalized Neyman-Pearson framework to identify the optimal forms of the solutions. We then develop a dual formulation and show that the infinite-dimensional constrained optimization problems can be reduced to finite-dimensional unconstrained ones. With the support of the Nelder-Mead algorithm, we are able to obtain optimal solutions efficiently. We illustrate the versatility of our approach by working out several detailed numerical examples, many of which in the literature were only partially resolved.

Suggested Citation

  • Cheung, Ka Chun & He, Wanting & Wang, He, 2023. "Multi-constrained optimal reinsurance model from the duality perspectives," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 199-214.
    • Handle: RePEc:eee:insuma:v:113:y:2023:i:c:p:199-214
    DOI: 10.1016/j.insmatheco.2023.08.003
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    More about this item

    Keywords

    Optimal reinsurance; Generalized Neyman-Pearson lemma; Distortion risk measure; Duality;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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