Optimal Reinsurance with Multiple Reinsurers: Competitive Pricing and Coalition Stability

29 Pages Posted: 22 Mar 2018

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: January 8, 2018

Abstract

We study economic pricing of reinsurance contracts via competition of an insurer with multiple reinsurers. All firms are endowed with distortion risk measures or expected exponential utilities. We require that contracts are Pareto optimal, individually rational, and satisfy a competition constraint that we call coalition stability. Indemnities are characterized by imposing Pareto optimality, as studied in the literature. In this paper, we characterize the corresponding premiums. There is a gain for the insurer due to the competition constraint. When the firms use distortion risk measures, this constraint yields stability for subcoalitions, which is a condition akin to the core in cooperative game theory. We show this gain for the insurer in closed form. Then, we derive that the premium is represented by a distortion premium function. If the firms use expected exponential utilities, the premium is represented by an exponential premium. We illustrate this premium function with the Mean Conditional Value-at-Risk.

Keywords: reinsurance, multiple reinsurers, competition, premiums, Mean Conditional Value-at-Risk

Suggested Citation

Boonen, Tim J. and Tan, Ken Seng and Zhuang, Sheng Chao, Optimal Reinsurance with Multiple Reinsurers: Competitive Pricing and Coalition Stability (January 8, 2018). Available at SSRN: https://ssrn.com/abstract=3143224 or http://dx.doi.org/10.2139/ssrn.3143224

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

Ken Seng Tan

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Sheng Chao Zhuang

University of Nebraska Lincoln ( email )

Lincoln, NE 68588
United States
4024722330 (Phone)

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