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A stochastic representation theorem with applications to optimization and obstacle problems. (English) Zbl 1058.60022

Authors’ summary: We study a new type of representation problem for optional processes with connections to singular control, optimal stopping and dynamic allocation problems. As an application, we show how to solve a variant of Skorokhod’s obstacle problem in the context of backward stochastic differential equations.

MSC:

60G07 General theory of stochastic processes
60G40 Stopping times; optimal stopping problems; gambling theory
60H25 Random operators and equations (aspects of stochastic analysis)
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