Optimal Reinsurance with One Insurer and Multiple Reinsurers

27 Pages Posted: 11 Jul 2015

See all articles by Tim J. Boonen

Tim J. Boonen

University of Amsterdam

Ken Seng Tan

University of Waterloo

Sheng Chao Zhuang

University of Nebraska Lincoln

Date Written: June 1, 2015

Abstract

In this paper, we consider a one-period optimal reinsurance design model with n reinsurers and an insurer. For very general preferences of the insurer, we obtain that there exists a very intuitive pricing formula for all reinsurers that use a distortion premium principle. The insurer determines its optimal risk that it wants to reinsure via this pricing formula. This risk it wants to reinsure is then shared by the reinsurers via tranching. The optimal ceded loss functions among multiple reinsurers are derived explicitly under the additional assumptions that the insurer’s preferences are given by an inverse-S shaped distortion risk measure and that the reinsurer’s premium principles are some functions of the Conditional Value-at-Risk. We also demonstrate that under some prescribed conditions, it is never optimal for the insurer to cede its risk to more than two reinsurers.

Keywords: optimal reinsurance design, distortion risk measure, distortion premium principle, multiple reinsurers, representative reinsurer

Suggested Citation

Boonen, Tim J. and Tan, Ken Seng and Zhuang, Sheng Chao, Optimal Reinsurance with One Insurer and Multiple Reinsurers (June 1, 2015). Available at SSRN: https://ssrn.com/abstract=2628950 or http://dx.doi.org/10.2139/ssrn.2628950

Tim J. Boonen

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

Ken Seng Tan (Contact Author)

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Sheng Chao Zhuang

University of Nebraska Lincoln ( email )

Lincoln, NE 68588
United States
4024722330 (Phone)

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
146
Abstract Views
1,005
rank
242,003
PlumX Metrics