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OPTIMAL REINSURANCE FROM THE PERSPECTIVES OF BOTH AN INSURER AND A REINSURER

Published online by Cambridge University Press:  14 December 2015

Jun Cai ,
Christiane Lemieux  and
Fangda Liu
Jun Cai
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada Email: [email protected]
Christiane Lemieux
Affiliation:
Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada Email: [email protected]
Fangda Liu*
Affiliation:
China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, 100081, China Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, N2L 3G1 Ontario, Canada
*
Email: [email protected]
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Abstract

Optimal reinsurance from an insurer's point of view or from a reinsurer's point of view has been studied extensively in the literature. However, as two parties of a reinsurance contract, an insurer and a reinsurer have conflicting interests. An optimal form of reinsurance from one party's point of view may be not acceptable to the other party. In this paper, we study optimal reinsurance designs from the perspectives of both an insurer and a reinsurer and take into account both an insurer's aims and a reinsurer's goals in reinsurance contract designs. We develop optimal reinsurance contracts that minimize the convex combination of the Value-at-Risk (VaR) risk measures of the insurer's loss and the reinsurer's loss under two types of constraints, respectively. The constraints describe the interests of both the insurer and the reinsurer. With the first type of constraints, the insurer and the reinsurer each have their limit on the VaR of their own loss. With the second type of constraints, the insurer has a limit on the VaR of his loss while the reinsurer has a target on his profit from selling a reinsurance contract. For both types of constraints, we derive the optimal reinsurance forms in a wide class of reinsurance policies and under the expected value reinsurance premium principle. These optimal reinsurance forms are more complicated than the optimal reinsurance contracts from the perspective of one party only. The proposed models can also be reduced to the problems of minimizing the VaR of one party's loss under the constraints on the interests of both the insurer and the reinsurer.

Keywords

Optimal reinsurancevalue-at-riskinsurer's lossreinsurer's profitexpected value reinsurance principle
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 46 , Issue 3 , September 2016 , pp. 815 - 849
Copyright
Copyright © Astin Bulletin 2015 

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References

Asimit, A.V., Badescu, A.M. and Cheung, K.C. (2013a) Optimal reinsurance in the presence of counterparty default risk. Insurance: Mathematics and Economics, 53 (3), 590–697.Google Scholar
Asimit, A.V., Badescu, A.M. and Verdoncj, T. (2013b) Optimal risk transfer under quantile-based risk measures. Insurance: Mathematics and Economics, 53 (1), 252–265.Google Scholar
Balbás, A., Balbás, B., Balbás, R. and Heras, A. (2015) Optimal reinsurance under risk and uncertainty. Insurance: Mathematics and Economics, 60, 61–74.Google Scholar
Balbás, A., Balbás, B. and Heras, A. (2009) Optimal reinsurance with general risk measures. Insurance: Mathematics and Economics, 44 (3), 374–384.Google Scholar
Balbás, A., Balbás, B. and Heras, A. (2011) Stable solutions for optimal reinsurance problems involving risk measures. European Journal of Operational Research, 214 (3), 796–804.Google Scholar
Borch, K. (1960) Reciprocal reinsurance treaties seen as a two-person co-operative game. Scandinavian Actuarial Journal, 1960 (1), 29–58.Google Scholar
Borch, K. (1969) The optimal reinsurance treaty. ASTIN Bulletin, 5 (2) 293–297.Google Scholar
Cai, J., Fang, Y., Li, Z. and Willmot, G.E. (2013) Optimal reciprocal reinsurance treaties under the joint survival probability and the joint profitable probability. Journal of Risk and Insurance 80 (1), 145–168.Google Scholar
Cai, J., Lemieux, C. and Liu, F. (2014) Optimal reinsurance with regulatory initial capital and default risk. Insurance: Mathematics and Economics, 57 (3), 13–24.Google Scholar
Cai, J. and Tan, K.S. (2007) Optimal retention for a stop-loss reinsurance under the VaR and CTE risk measures. ASTIN Bulletin, 37 (1), 93–112.Google Scholar
Cai, J. and Wei, W. (2012) Optimal reinsurance with positively dependent risks. Insurance: Mathematics and Economics, 50 (1), 57–63.Google Scholar
Cheung, K.C. (2010) Optimal reinsurer revisited - a geometric approach. ASTIN Bulletin, 40 (1), 221–239.Google Scholar
Cheung, K.C., Sung, K.C.J. and Yam, S.C.P. (2014a) Risk-minimizing reinsurance protection for multivariate risks. Journal of Risk and Insurance, 81 (1), 219–236.CrossRefGoogle Scholar
Cheung, K.C., Sung, K. C. J., Yam, S. C. P. and Yung, S.P. (2014b) Optimal reinsurance under general law-invariant risk measures. Scandinavian Actuarial Journal, 2014 (1), 72–91.Google Scholar
Chi, Y. (2012) Reinsurance arrangements minimizing the risk-adjusted value of an insurer's liability. ASTIN Bulletin, 42 (2), 529–557.Google Scholar
Chi, Y. and Meng, H. (2014) Optimal reinsurance arrangements in the presence of two reinsurers. Scandinavian Actuarial Journal, 2014 (5), 424–438.Google Scholar
Chi, Y. and Tan, K.S. (2011) Optimal reinsurance under VaR and CVaR risk measures: A simplified approach. ASTIN Bulletin, 41 (2), 487–509.Google Scholar
Fang, Y. and Qu, Z. (2014) Optimal combination of quota-share and stop-loss reinsurance treaties under the joint survival probability. IMA Journal of Management Mathematics, 25 (1), 89–103.CrossRefGoogle Scholar
Hürlimann, W. (2011) Optimal reinsurance revisited - point of view of cedent and reinsurer. ASTIN Bulletin, 41 (2), 547–574.Google Scholar