The Annals of Probability

A stochastic representation theorem with applications to optimization and obstacle problems

Peter Bank and Nicole El Karoui

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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 Skorohod's obstacle problem in the context of backward stochastic differential equations.

Article information

Ann. Probab., Volume 32, Number 1B (2004), 1030-1067.

First available in Project Euclid: 11 March 2004

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Zentralblatt MATH identifier

Primary: 60G07: General theory of processes 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60H25: Random operators and equations [See also 47B80]

Representation problem for optional processes singular control optimal stopping Gittins index Skorohod problem inhomogeneous convexity


Bank, Peter; El Karoui, Nicole. A stochastic representation theorem with applications to optimization and obstacle problems. Ann. Probab. 32 (2004), no. 1B, 1030--1067. doi:10.1214/aop/1079021471.

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