Multi-constrained optimal reinsurance model from the duality perspectives

Cheung，Ka Chun1; He，Wanting1; Wang，He2

2023-11-01

10.1016/j.insmatheco.2023.08.003

Insurance: Mathematics and Economics   Impact Factor & Quartile

0167-6687

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.

Distortion risk measure Duality Generalized Neyman-Pearson lemma Optimal reinsurance

English

Others

ECONOMICS BUSINESS

2-s2.0-85170704580

Scopus

1.Department of Statistics and Actuarial Science,The University of Hong Kong,Pokfulam Road,Hong Kong
2.Department of Finance,Southern University of Science and Technology,Shenzhen,Xueyuan Road,China

Cheung，Ka Chun,He，Wanting,Wang，He. Multi-constrained optimal reinsurance model from the duality perspectives[J]. Insurance: Mathematics and Economics,2023,113:199-214.

Cheung，Ka Chun,He，Wanting,&Wang，He.(2023).Multi-constrained optimal reinsurance model from the duality perspectives.Insurance: Mathematics and Economics,113,199-214.

Cheung，Ka Chun,et al."Multi-constrained optimal reinsurance model from the duality perspectives".Insurance: Mathematics and Economics 113(2023):199-214.