Time-consistent investment-reinsurance strategies towards joint interests of the insurer and the reinsurer under CEV models  

作　　者：ZHAO Hui WENG ChengGuo SHEN Yang ZENG Yan 

机构地区：[1]School of Science, Tianjin University, Tianjin 300072, China [2]Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3GI, Canada [3]Department of Mathematics and Statistics, York University, Toronto, ON M3J IP3, Canada [4]Lingnan (University) College, Sun Yat-sen University, Guangzhou 510275, China

出　　处：《Science China Mathematics》2017年第2期317-344,共28页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11301376, 71201173 and 71571195);China Scholarship Council, the Natural Sciences and Engineering Research Council of Canada (NSERC);Society of Actuaries Centers of Actuarial Excellence Research Grant, Guangdong Natural Science Funds for Distinguished Young Scholar (Grant No. 2015A030306040);Natural Science Foundation of Guangdong Province of China (Grant No. 2014A030310195);for Ying Tung Eduction Foundation for Young Teachers in the Higher Education Institutions of China (Grant No. 151081)

摘　　要：The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework.The paper is distinguished from other literature by taking into account the interests of both an insurer and a reinsurer jointly.The claim process of the insurer is governed by a Brownian motion with a drift.A proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle.Both the insurer and the reinsurer are assumed to invest in a risky asset,which is distinct for each other and driven by a constant elasticity of variance model.The optimal decision is formulated on a weighted sum of the insurer’s and the reinsurer’s surplus processes.Upon a verification theorem,which is established with a formal proof for a more general problem,explicit solutions are obtained for the proposed investment-reinsurance model.Moreover,numerous mathematical analysis and numerical examples are provided to demonstrate those derived results as well as the economic implications behind.The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework. The paper is distinguished from other literature by taking into account the interests of both an insurer and a reinsurer jointly. The claim process of the insurer is governed by a Brownian motion with a drift. A proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle. Both the insurer and the reinsurer are assumed to invest in a risky asset, which is distinct for each other and driven by a constant elasticity of variance model. The optimal decision is formulated on a weighted sum of the insurer＇s and the reinsurer＇s surplus processes. Upon a verification theorem, which is established with a formal proof for a more general problem, explicit solutions are obtained for the proposed investment-reinsurance model. Moreover, numerous mathematical analysis and numerical examples are provided to demonstrate those derived results as well as the economic implications behind.

关 键 词：investment-reinsurance problem mean-variance analysis time-consistent strategy constant elas-ticity of variance model 

分 类 号：F840.6[经济管理—保险] F224