带交易费用和投资约束的扩散模型中最优投资-分红问题

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 corporation 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.