Let us consider the scenario tree of Fig. 11.10 and define consider decision 

Data From Fig. 11.10

Data From Example 11.17

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cision variables Z and Z, representing the number of stock shares that we buy and sell, respectively, at time t. At time t = 0, we have a unique decision, since we can just buy or sell, here and now. From the perspective at time t = 0, the decisions made at the next time in- stants are random variables, as they depend on the observed path of the stochastic process and the expectations about the future, which are encoded in the scenario tree. The random variables at time t must be F+-measurable. If we are at node n in the scenario tree of Fig. 11.10, we cannot say "buy if scenario is w3" and "do not buy if scenario is W4." The decision, whatever it is, must be the same for the two sce- narios w3 and w4. Otherwise, the random variable corresponding to the decision at that node would not be constant over the outcomes in- cluded the event {w3, w4}, and it would not be measurable; we would be in the same trouble as in Example 11.17.