Optimal dividend and capital injection problem with a random time horizon and a ruin penalty in the dual model  

作　　者：ZHAO Yong-xia YAO Ding-jun 

机构地区：[1]School of Statistics, Qufu Normal University [2]School of Finance, Nanjing University of Finance and Economics

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2015年第3期325-339,共15页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11231005);Promotive research fund for excellent young and middle-aged scientists of Shandong Province(BS2014SF006);the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(15KJB110009)

摘　　要：In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, and the penalized discounted both capital injections and ruin penalty during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. The explicit solutions for optimal strategy and value function are obtained, when the income jumps follow a hyper-exponential distribution.Besides, some numerical examples are presented to illustrate our results.In the dual risk model, we consider the optimal dividend and capital injection problem, which involves a random time horizon and a ruin penalty. Both fixed and proportional costs from the transactions of capital injection are considered. The objective is to maximize the total value of the expected discounted dividends, and the penalized discounted both capital injections and ruin penalty during the horizon, which is described by the minimum of the time of ruin and an exponential random variable. The explicit solutions for optimal strategy and value function are obtained, when the income jumps follow a hyper-exponential distribution.Besides, some numerical examples are presented to illustrate our results.

关 键 词：dual model transaction cost DIVIDEND capital injection HJB equation 

分 类 号：F832.51[经济管理—金融学] F224