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On a Class of Infinite-Dimensional Singular Stochastic Control Problems
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2021-04-21 , DOI: 10.1137/20m136757x Salvatore Federico , Giorgio Ferrari , Frank Riedel , Michael Röckner
SIAM Journal on Control and Optimization ( IF 2.2 ) Pub Date : 2021-04-21 , DOI: 10.1137/20m136757x Salvatore Federico , Giorgio Ferrari , Frank Riedel , Michael Röckner
SIAM Journal on Control and Optimization, Volume 59, Issue 2, Page 1680-1704, January 2021.
We study a class of infinite-dimensional singular stochastic control problems that might find applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially ordered infinite-dimensional space $X$, it takes values in the positive cone of $X$, and it has right-continuous and nondecreasing paths. Our main contribution is to provide a rigorous formulation of the problem by properly defining the controlled dynamics and integrals with respect to the control process, and then to derive necessary and sufficient first-order conditions for optimality. The latter are finally exploited in a specification of the model where we determine an optimal control. The techniques used are those of semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.
中文翻译：
关于一类无穷维奇异随机控制问题
SIAM控制与优化杂志，第59卷，第2期，第1680-1704页，2021年1月。
我们研究了一类无穷维奇异随机控制问题，这些问题可能会在经济理论和金融领域得到应用。控制过程线性地影响了适当的部分有序无穷维空间$ X $上的抽象演化方程，它的取值在$ X $的正圆锥中，并且具有右连续且不递减的路径。我们的主要贡献是通过正确地定义相对于控制过程的受控动力学和积分来提供对问题的严格表述，然后得出最优的必要和足够的一阶条件。最终在模型的规范中利用了后者，在此我们确定了最佳控制。使用的技术包括半群理论，向量值积分，凸分析，
更新日期：2021-04-23
We study a class of infinite-dimensional singular stochastic control problems that might find applications in economic theory and finance. The control process linearly affects an abstract evolution equation on a suitable partially ordered infinite-dimensional space $X$, it takes values in the positive cone of $X$, and it has right-continuous and nondecreasing paths. Our main contribution is to provide a rigorous formulation of the problem by properly defining the controlled dynamics and integrals with respect to the control process, and then to derive necessary and sufficient first-order conditions for optimality. The latter are finally exploited in a specification of the model where we determine an optimal control. The techniques used are those of semigroup theory, vector-valued integration, convex analysis, and general theory of stochastic processes.
中文翻译：
关于一类无穷维奇异随机控制问题
SIAM控制与优化杂志，第59卷，第2期，第1680-1704页，2021年1月。
我们研究了一类无穷维奇异随机控制问题，这些问题可能会在经济理论和金融领域得到应用。控制过程线性地影响了适当的部分有序无穷维空间$ X $上的抽象演化方程，它的取值在$ X $的正圆锥中，并且具有右连续且不递减的路径。我们的主要贡献是通过正确地定义相对于控制过程的受控动力学和积分来提供对问题的严格表述，然后得出最优的必要和足够的一阶条件。最终在模型的规范中利用了后者，在此我们确定了最佳控制。使用的技术包括半群理论，向量值积分，凸分析，
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