  Complexity and uncertainty associated with commodity resource valuation and
extraction requires stochastic control methods suitable for high dimensional
states. Recent progress in duality and trajectory-wise techniques has
introduced a variety of fresh ideas to this field with surprising results. This
paper presents a first application of this promising development to commodity
extraction problems. We introduce efficient algorithms for obtaining
approximate solutions along with a diagnostic technique, which provides a
quantitative measure for solution performance in terms of the distance between
the approximate and the optimal control policy.
