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

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.