论文标题
通过受控随机化和相关的倾斜反射BSDS切换问题
Switching problems with controlled randomisation and associated obliquely reflected BSDEs
论文作者
论文摘要
我们介绍并研究了一类新的最佳切换问题，即通过受控的随机性切换问题，其中一些随机性会影响切换模式和相关成本的选择。我们表明，开关问题的最佳值与一类新的多维BSDE相关。这些BSDE还允许构建最佳策略，从而完全解决初始问题。我们工作的另一个主要贡献是证明这些倾斜反射的BSDE的新存在和独特结果。这是通过仔细研究反射领域和适当的倾斜反射操作员的构建来实现的，以便从[7]引用结果。
We introduce and study a new class of optimal switching problems, namely switching problem with controlled randomisation, where some extra-randomness impacts the choice of switching modes and associated costs. We show that the optimal value of the switching problem is related to a new class of multidimensional obliquely reflected BSDEs. These BSDEs allow as well to construct an optimal strategy and thus to solve completely the initial problem. The other main contribution of our work is to prove new existence and uniqueness results for these obliquely reflected BSDEs. This is achieved by a careful study of the domain of reflection and the construction of an appropriate oblique reflection operator in order to invoke results from [7].
