带交易费用和投资约束的扩散模型中最优投资-分红问题（英文）  

Optimization of Investment-Dividend Problem in a Diffusion Model with Transaction Costs and Investment Constraints

作　　者：李曼曼[1] 刘再明[2] 

机构地区：[1]重庆大学数学与统计学院统计与精算学系,重庆401331 [2]中南大学数学与统计学院概率统计研究所,长沙410083

出　　处：《应用概率统计》2017年第2期151-169,共19页Chinese Journal of Applied Probability and Statistics

基　　金：partly supported by the Project of the Humanities and Social Sciences of the Ministry of Education to the West and the Border Areas(Grant No.14XJC910001);the Fundamental Research Funds for the Central Universities(Grant No.106112016CDJXY100002);the National Natural Science Foundation of China(Grant No.11671404)

摘　　要：本文研究了带交易费用和投资约束的最优投资-分红问题.假定公司投资受到包含卖空和借贷的一般性约束条件,由此产生正则-脉冲随机控制问题.本文重点研究了投资收入不能满足资本折扣损失的非平凡情形,区分了三种不同可能状况下的拟变分不等式,并构造了其对应的值函数和最优策略.我们最后也给出了平凡情形下随机控制的具体结论.This paper investigates the investment-dividend optimization problem for a corpora- tion with transaction costs and investment constraints. The main feature is that we assume general constraints on investments including the special case of short-sale and borrowing constraints. This results in a regular-impulse stochastic control problem. The nontrivial case is that the investment can＇t meet the loss of wealth due to discounting. In this case, delicate analysis is carried out on QVI w.r.t, three possible situations, leading to an explicit construction of the value functions together with the optimal policies. We also give explicit conclusion of the trivial case at last.

关 键 词：投资约束 交易费用 正则-脉冲控制 拟变分不等式 

分 类 号：O212.6[理学—概率论与数理统计]