A GENERAL VERIFICATION RESULT FOR STOCHASTIC IMPULSE CONTROL PROBLEMS

被引:21
作者
Belak, Christoph [1 ]
Christensen, Soeren [2 ]
Seifried, Frank Thomas [1 ]
机构
[1] Univ Trier, Dept Math 4, Univ Sring 19, D-54296 Trier, Germany
[2] Univ Hamburg, Dept Math, SPST, Bundesstr 55, D-20146 Hamburg, Germany
关键词
impulse control; stochastic Perron; superharmonic functions; optimal controls; PROPORTIONAL TRANSACTION COSTS; MULTIDIMENSIONAL JUMP DIFFUSIONS; PERRONS METHOD; DEGENERATE DIFFUSIONS; OPTIMIZATION PROBLEMS; EXCHANGE-RATE; GAMES; PORTFOLIO; STRATEGIES; EQUATIONS;
D O I
10.1137/16M1082822
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
This paper establishes existence of optimal controls for a general stochastic impulse control problem. For this, the value function is characterized as the pointwise minimum of a set of superharmonic functions, as the unique continuous viscosity solution of the quasi-variational inequalities (QVIs), and as the limit of a sequence of iterated optimal stopping problems. A combination of these characterizations is used to construct optimal controls without relying on any regularity of the value function beyond continuity. Our approach is based on the stochastic Perron method and the assumption that the associated QVIs satisfy a comparison principle.
引用
收藏
页码:627 / 649
页数:23
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