= Singular consumption control
{title2=$dw=\cdots-dC,\quad d\xi=-\lambda\xi\,dt+dC$}
In <singular stochastic control>, an unrestricted <consumption> rate can approximate instantaneous transfers from <portfolio wealth> into a <consumption satisfaction stock>. In the relaxed problem a nondecreasing control $C$ records these transfers. A transfer $\Delta C$ decreases <portfolio wealth> and increases <consumption satisfaction> by the same amount. Rate controls need not attain the supremum when the relaxed optimum has a jump.
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