有限时间范围上的多维奇异随机控制问题

Annales Umcs, Mathematica Pub Date : 2015-11-30 DOI:10.17951/A.2015.69.1.23

A. Sectio, Marcin Boryc, Łukasz Kruk

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引用次数: 0

摘要

研究了有限时间范围上n维含时间相关系数的奇异随机控制问题。我们证明了这个问题的值函数是相应的HJB方程的广义解，它对空间变量具有局部有界的二阶导数，对时间具有局部有界的一阶导数。此外，我们还证明了最优控制的存在性和唯一性。

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A multidimensional singular stochastic control problem on a finite time horizon

A singular stochastic control problem in n dimensions with timedependent coefficients on a finite time horizon is considered. We show that the value function for this problem is a generalized solution of the corresponding HJB equation with locally bounded second derivatives with respect to the space variables and the first derivative with respect to time. Moreover, we prove that an optimal control exists and is unique.

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Annales Umcs, Mathematica

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