Regularity of the value function for a two-dimensional singular stochastic control problem
Regularity of the value function for a two-dimensional singular stochastic control problem
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DOI：
10.1137/0327047
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发表时间：
1989-07
影响因子：
2.2
通讯作者：
-H.;Mete Soner;Steven;-E.;Shreve
中科院分区：
文献类型：
--
作者：
-H.;Mete Soner;Steven;-E.;Shreve
希望通过向其添加（可能是奇异的）连续过程来控制二维布朗运动，以便最小化预期的无限范围折扣运行成本。价值函数 V 的 Hamilton-Jacobi-Bellman 表征是一个变分不等式，具有唯一的两次连续可微解。通过求解沿 $ - \nabla V$ 方向的自由边界反映二维布朗运动的 Skorokhod 问题来构建最优控制过程。
It is desired to control a two-dimensional Brownian motion by adding a (possibly singularly) continuous process to it so as to minimize an expected infinite-horizon discounted running cost. The Hamilton–Jacobi–Bellman characterization of the value function V is a variational inequality which has a unique twice continuously differentiable solution. The optimal control process is constructed by solving the Skorokhod problem of reflecting the two-dimensional Brownian motion along a free boundary in the $ - \nabla V$ direction.