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

See all articles by Tim J. Boonen

Tim J. Boonen

University of Amsterdam

Mario Ghossoub

University of Waterloo

Date Written: June 8, 2020

Abstract

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

Boonen, Tim J. and Ghossoub, Mario, Optimal Reinsurance with Multiple Reinsurers: Distortion Risk Measures, Distortion Premium Principles, and Heterogeneous Beliefs (June 8, 2020). Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=3475657 or http://dx.doi.org/10.2139/ssrn.3475657

Tim J. Boonen (Contact Author)

University of Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

HOME PAGE: http://www.uva.nl/profiel/b/o/t.j.boonen/t.j.boonen.html

Mario Ghossoub

University of Waterloo ( email )

Dept. of Statistics & Actuarial Science
200 University Ave. W.
Waterloo, Ontario N2L 3G1
Canada

HOME PAGE: http://uwaterloo.ca/scholar/mghossou

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