A Class of Solvable Impulse Control Problems
A Class of Solvable Impulse Control Problems
复制标题
一类可解决的脉冲控制问题
DOI：
10.1007/s00245-004-0792-z
复制
发表时间：
2004
影响因子：
1.8
通讯作者：
L. Alvarez
中科院分区：
文献类型：
--
作者：
L. Alvarez
摘要
我们考虑一类随机脉冲控制
受控过程按照某个规律演化的问题
线性、规则和时间均匀扩散。我们陈述一组
容易验证问题出现的充分条件
明确可解。我们还给出了一个代数方程
可以确定最佳脉冲边界，并且给定
这个阈值，我们提出最优策略的值
最小递增 r-过度映射的项
受控扩散。我们还考虑了相对静态
最优策略的属性并陈述一组典型的
满足波动性增加的条件
明确地增加了最优策略的价值并且
扩大了行使不可逆性的延续区域
政策并不理想。我们还说明了我们的
在基于几何布朗运动的两个模型中得到明确的结果。
Abstract
We consider a class of stochastic impulse control
problems where the controlled process evolves according to a
linear, regular, and time homogeneous diffusion. We state a set of
easily verifiable sufficient conditions under which the problem is
explicitly solvable. We also state an algebraic equation from
which the optimal impulse boundary can be determined and, given
this threshold, we present the value of the optimal policy in
terms of the minimal increasing r-excessive mapping for the
controlled diffusion. We also consider the comparative static
properties of the optimal policy and state a set of typically
satisfied conditions under which increased volatility
unambiguously increases the value of the optimal policy and
expands the continuation region where exercising the irreversible
policy is suboptimal. We also illustrate our
results explicitly in two models based on geometric Brownian motion.