论文标题
随机折扣下的最佳股息支出
Optimal Dividend Payout under Stochastic Discounting
论文作者
论文摘要
采用概率方法，我们确定了一家公司的最佳股息支付政策，该公司的盈余流程遵循受控的算术布朗尼动议，其现金流量以随机的动态速度打折。可以以不受限制的利率将股息支付给股东，以便将问题作为奇异随机控制之一。随机利率是由Cox-Ingersoll-Ross（CIR）流程建模的，该公司的目标是最大化折扣股息的总预期流量，直到可能的破产时间为止。我们发现最佳的股息支付政策，即剩余过程保持在当前利率值的内源确定的随机阈值以下，其随机阈值表示为降低的连续函数$ r \ r \ mapsto b（r）$。我们还证明，奇异控制问题的价值函数解决了与二阶非分类椭圆运算符相关的变异不等式，并具有梯度约束。
Adopting a probabilistic approach we determine the optimal dividend payout policy of a firm whose surplus process follows a controlled arithmetic Brownian motion and whose cash-flows are discounted at a stochastic dynamic rate. Dividends can be paid to shareholders at unrestricted rates so that the problem is cast as one of singular stochastic control. The stochastic interest rate is modelled by a Cox-Ingersoll-Ross (CIR) process and the firm's objective is to maximize the total expected flow of discounted dividends until a possible insolvency time. We find an optimal dividend payout policy which is such that the surplus process is kept below an endogenously determined stochastic threshold expressed as a decreasing continuous function $r \mapsto b(r)$ of the current interest rate value. We also prove that the value function of the singular control problem solves a variational inequality associated to a second-order, non-degenerate elliptic operator, with a gradient constraint.
