Pareto-Optimal Reinsurance Arrangements Under General Model Settings

35 Pages Posted: 21 Dec 2016

See all articles by Jun Cai

Jun Cai

University of Waterloo - Department of Statistics and Actuarial Science

Haiyan Liu

Michigan State University - Department of Mathematics

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: December 19, 2016

Abstract

In this paper, we study Pareto optimality of reinsurance arrangements under general model settings. We give the necessary and sufficient conditions for a reinsurance contract to be Pareto-optimal and characterize all Pareto-optimal reinsurance contracts under more general model assumptions. We also obtain the sufficient conditions that guarantee the existence of the Pareto-optimal reinsurance contracts. When the losses of an insurer and a reinsurer are both measured by the Tail-Value-at-Risk (TVaR) risk measures, we obtain the explicit forms of the Pareto-optimal reinsurance contracts under the expected value premium principle. From the purpose of practice, we use numerical examples to show how to determine the best Pareto-optimal reinsurance contracts among the available Pareto-optimal reinsurance contracts such that both the insurer's aim and the reinsurer's goal can be met under the best Pareto-optimal reinsurance contracts.

Keywords: Pareto optimality, optimal reinsurance, comonotonic-semilinearity, comonotonic-convexity, Tail-Value-at-Risk

JEL Classification: C60; C710.

Suggested Citation

Cai, Jun and Liu, Haiyan and Wang, Ruodu, Pareto-Optimal Reinsurance Arrangements Under General Model Settings (December 19, 2016). Available at SSRN: https://ssrn.com/abstract=2887632 or http://dx.doi.org/10.2139/ssrn.2887632

Jun Cai

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Haiyan Liu (Contact Author)

Michigan State University - Department of Mathematics ( email )

619 Red Cedar Road
East Lansing, MI 48824
United States

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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