Alternative Approach to the Optimality of the Threshold Strategy for Spectrally Negative Lvy Processes  

作　　者：Ying SHEN Chuan-cun YIN Kam Chuen YUEN 

机构地区：[1]School of Mathematical Sciences,Qufu Normal University,China [2]Department of Statistics and Actuarial Science,The University of Hong Kong

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第4期705-716,共12页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10771119,No.11171179);the Research Fund for the Doctoral Program of Higher Education of China(No.20093705110002);The research of Kam C.Yuen was supported by a university research grant of the University of Hong Kong

摘　　要：Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. In this paper, we show that a threshold strategy （also called refraction strategy） forms an optimal strategy under the condition that the Levy measure has a completely monotone density.Consider the optimal dividend problem for an insurance company whose uncontrolled surplus precess evolves as a spectrally negative Levy process. We assume that dividends are paid to the shareholders according to admissible strategies whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. In this paper, we show that a threshold strategy （also called refraction strategy） forms an optimal strategy under the condition that the Levy measure has a completely monotone density.

关 键 词：Spectrally negative Levy process optimal dividend problem scale function complete monotonic-ity threshold strategy 

分 类 号：O224[理学—运筹学与控制论]