论文标题
De Finetti的控制问题与控制率的凹面
De Finetti's control problem with a concave bound on the control rate
论文作者
论文摘要
我们认为De Finetti的控制问题是绝对连续的策略，其控制速率受凹功能界定，并证明了广义的均值反复策略是最佳的。为了解决这个问题，我们需要处理非线性的Ornstein-Uhlenbeck过程。尽管对速率施加的界限的一般性水平，但在评估两个函数的情况下，获得了价值函数的明确表达。该最佳控制问题的控制速率分别受常数和线性函数的限制，如特殊情况。
We consider De Finetti's control problem for absolutely continuous strategies with control rates bounded by a concave function and prove that a generalized mean-reverting strategy is optimal. In order to solve this problem, we need to deal with a nonlinear Ornstein-Uhlenbeck process. Despite the level of generality of the bound imposed on the rate, an explicit expression for the value function is obtained up to the evaluation of two functions.This optimal control problem has those with control rates bounded by a constant and a linear function, respectively, as special cases.
