Optimal Reinsurance with Multiple Reinsurers: Distortion Risk Measures, Distortion Premium Principles, and Heterogeneous Beliefs
34 Pages Posted: 5 Nov 2019 Last revised: 8 Jun 2020
Date Written: June 8, 2020
This paper unifies the work on multiple reinsurers, distortion risk measures, premium budgets,
and heterogeneous beliefs. An insurer minimizes a distortion risk measure, while seeking
reinsurance with finitely many reinsurers. The reinsurers use distortion premium principles, and
they are allowed to have heterogeneous beliefs regarding the underlying probability distribution.
We provide a characterization of optimal reinsurance indemnities, and we show that they are of
a layer-insurance type. This is done both with and without a budget constraint, i.e., an upper
bound constraint on the aggregate premium. Moreover, the optimal reinsurance indemnities
enable us to identify a representative reinsurer in both situations. Finally, two examples with
the Conditional Value-at-Risk illustrate our results.
Keywords: Optimal reinsurance design, distortion risk measures, distortion premium principle, heterogeneous beliefs, multiple reinsurers
JEL Classification: D86, G22
Suggested Citation: Suggested Citation