Optimal Reinsurance from the Perspectives of Both Insurers and Reinsurers Under General Distortion Risk Measures

Abstract

In this article, we propose new methodologies to tackle and the problems studied in [Cai, J., Lemieux, C. and Liu, F., 2016, Optimal reinsurance from the perspectives of both an insurer and a reinsurer, ASTIN Bulletin, 46(3), 815-849]. Optimal reinsurance contracts that minimize the convex combination of the risk measurements of the insurer's loss and the reinsurer's loss are characterized under different types of constraints. The results in Cai et al. (2016) are considerably extended to the general framework of distortion risk measures and distortion premium principle.