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.
"A stochastic representation theorem with applications to optimization and obstacle problems." Ann. Probab. 32 (1B) 1030 - 1067, January 2004. https://doi.org/10.1214/aop/1079021471