Time-Consistent Investment-Reinsurance Strategies for the Insurer and the Reinsurer under the Generalized Mean-Variance Criteria

Helu Xiao, Tiantian Ren, Yanfei Bai and Zhongbao Zhou
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Helu Xiao: School of Business, Hunan Normal University, Changsha 410081, China
Tiantian Ren: School of Business Administration, Hunan University, Changsha 410082, China
Yanfei Bai: School of Business Administration, Hunan University, Changsha 410082, China
Zhongbao Zhou: School of Business Administration, Hunan University, Changsha 410082, China

Mathematics, 2019, vol. 7, issue 9, 1-25

Abstract: Most of the existing literature on optimal investment-reinsurance only studies from the perspective of insurers and also treats the investment-reinsurance decision as a continuous process. However, in practice, the benefits of reinsurers cannot be ignored, nor can decision-makers engage in continuous trading. Under the discrete-time framework, we first propose a multi-period investment-reinsurance optimization problem considering the joint interests of the insurer and the reinsurer, among which their performance is measured by two generalized mean-variance criteria. We derive the time-consistent investment-reinsurance strategies for the proposed model by maximizing the weighted sum of the insurer’s and the reinsurer’s mean-variance objectives. We discuss the time-consistent investment-reinsurance strategies under two special premium principles. Finally, we provide some numerical simulations to show the impact of the intertemporal restrictions on the time-consistent investment-reinsurance strategies. These results indicate that the intertemporal restrictions will urge the insurer and the reinsurer to shrink the position invested in the risky asset; however, for the time-consistent reinsurance strategy, the impact of the intertemporal restrictions depends on who is the leader in the proposed model.

Keywords: investment and reinsurance; insurer and reinsurer; generalized mean-variance criteria; time-consistent strategy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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