数学研究通讯

2015, v.31(03) 242-252

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A Mean-variance Problem in the Constant Elasticity of Variance(CEV) Model
A Mean-variance Problem in the Constant Elasticity of Variance(CEV) Model

Hou Ying-li;Liu Guo-xin;Jiang Chun-lan;

摘要(Abstract):

In this paper, we focus on a constant elasticity of variance(CEV) model and want to find its optimal strategies for a mean-variance problem under two constrained controls: reinsurance/new business and investment(no-shorting). First, a Lagrange multiplier is introduced to simplify the mean-variance problem and the corresponding Hamilton-Jacobi-Bellman(HJB) equation is established. Via a power transformation technique and variable change method, the optimal strategies with the Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem,the optimal strategies and optimal value for the original problem(i.e., the efficient strategies and efficient frontier) are derived explicitly.

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基金项目(Foundation): The NSF(11201111) of China;; Hebei Province Colleges and Universities Science,and Technology Research Project(ZD20131017)

作者(Author): Hou Ying-li;Liu Guo-xin;Jiang Chun-lan;

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