Multi-Constrained Optimal Reinsurance Model from the Generalized Neyman-Pearson and the Daulity Perspectives

33 Pages Posted: 7 Nov 2022

See all articles by Ka Chun Cheung

Ka Chun Cheung

The University of Hong Kong

Wanting He

The University of Hong Kong

He Wang

Southern University of Science and Technology

Abstract

In the presence of multiple constraints such as the risk tolerance constraint and the budget constraint, the extensively studied general insurer-reinsurer symbiotic optimal reinsurance problems become technically challenging, and have only been solved using ad hoc yet tedious methods for certain special cases. In this paper, we propose a constructive generalized Neyman-Pearson framework to identify the optimal forms of the solutions. We then develop the dual formulation and show that such 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 under the most general settings. We illustrate the versatility and superiority of our approach by working out several detailed numerical examples, many of which in the literature were only partially resolved using more complicated techniques and impractical assumptions.

Keywords: Optimal Reinsurance, Generalized Neyman-Pearson Lemma, Distortion Risk Measure, Duality.

Suggested Citation

Cheung, Ka Chun and He, Wanting and Wang, He, Multi-Constrained Optimal Reinsurance Model from the Generalized Neyman-Pearson and the Daulity Perspectives. Available at SSRN: https://ssrn.com/abstract=4270407 or http://dx.doi.org/10.2139/ssrn.4270407

Ka Chun Cheung

The University of Hong Kong ( email )

Pokfulam Road
Hong Kong, Pokfulam HK
China

Wanting He (Contact Author)

The University of Hong Kong ( email )

Pokfulam Road
Hong Kong, HK
China

He Wang

Southern University of Science and Technology ( email )

1088 Xueyuan Avenue
Shenzhen, Guangdong 518055
China

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