  The paper introduces a limit version of multiple stopping options such that
the holder selects dynamically a weight function that control the distribution
of the payments (benefits) over time. In applications for commodities and
energy trading, a control process can represent the quantity that can be
purchased by a fixed price at current time. In another example, the control
represents the weight of the integral in a modification of the Asian option.
The pricing for these options requires to solve a stochastic control problem.
Some existence results and pricing rules are obtained via modifications of
parabolic Bellman equations.
