On the Existence of a Representative Reinsurer Under Heterogeneous Beliefs

36 Pages Posted: 1 Jan 2019 Last revised: 31 Jul 2019

See all articles by Tim J. Boonen

Tim J. Boonen

University of Amsterdam

Mario Ghossoub

University of Waterloo

Date Written: July 30, 2019

Abstract

This paper studies a one-period optimal reinsurance design model with n reinsurers and an insurer. The reinsurers are endowed with expected-value premium principles and with heterogeneous beliefs regarding the underlying distribution of the insurer’s risk. Under general preferences for the insurer, a representative reinsurer is characterized. This means that all reinsurers can be treated collectively by means of a hypothetical premium principle in order to determine the optimal total risk that is ceded to all reinsurers. The optimal total ceded risk is then allocated to the reinsurers by means of an explicit solution. This is shown both in the general case and under the no-sabotage condition that avoids possible ex post moral hazard on the side of the insurer, thereby extending the results of Boonen et al. (2016). We subsequently derive closed-form optimal reinsurance contracts in case the insurer maximizes expected net wealth. Moreover, under the no-sabotage condition, we derive optimal reinsurance contracts in case the insurer maximizes dual utility, or in case the insurer maximizes a generic objective that preserves second-order stochastic dominance under the assumption of a monotone hazard ratio.

Keywords: optimal reinsurance design, heterogeneous beliefs, multiple reinsurers, representative reinsurer, deductible

JEL Classification: D86, G22

Suggested Citation

Boonen, Tim J. and Ghossoub, Mario, On the Existence of a Representative Reinsurer Under Heterogeneous Beliefs (July 30, 2019). Available at SSRN: https://ssrn.com/abstract=3300773 or http://dx.doi.org/10.2139/ssrn.3300773

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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