On the existence of a representative reinsurer under heterogeneous beliefs

Tim J. Boonen; Mario Ghossoub

doi:10.1016/j.insmatheco.2019.07.008

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On the existence of a representative reinsurer under heterogeneous beliefs

Journal article

Peer reviewed

On the existence of a representative reinsurer under heterogeneous beliefs

Tim J. Boonen and Mario Ghossoub

Insurance, mathematics & economics, Vol.88, pp.209-225

09/01/2019

DOI: 10.1016/j.insmatheco.2019.07.008

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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. (C) 2019 Elsevier B.V. All rights reserved.

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Details

Title: Subtitle: On the existence of a representative reinsurer under heterogeneous beliefs
Creators: Tim J. Boonen - University of Amsterdam
Mario Ghossoub - University of Waterloo
Resource Type: Journal article
Publication Details: Insurance, mathematics & economics, Vol.88, pp.209-225
DOI: 10.1016/j.insmatheco.2019.07.008
ISSN: 0167-6687
eISSN: 1873-5959
Publisher: Elsevier
Number of pages: 17
Grant note: 2018-03961 / Natural Sciences and Engineering Research Council of Canada(NSERC); Natural Sciences and Engineering Research Council of Canada (NSERC)
Language: English
Date published: 09/01/2019
Academic Unit: Statistics and Actuarial Science
Record Identifier: 9985179965102771

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