One then applies the same procedure to the smaller network, obtaining a set S 1 . Removing nodes in S 1 from R 1 gives a yet smaller network, whose nodes we call R 2 . After creating , create . Since AMPL can not build infinitely many sets, think of the largest value that M might be. This puts us in position to use our DP formulation to find the cheapest path from each node to stage 0.
H is farthest in the future.
The optimal value is if and only if an arbitrage opportunity exists. We saw that these constraints can be useful in determining the window of prices for a new financial instrument which are consistent with the prices of instruments already on the market, i.e., the window of prices that do not create an arbitrage opportunity. Then we know that the window for the price p is non-empty. We discussed in lecture that the feasible points y for the above dual constraints can be thought of as giving probabilities with respect to which the value of a financial instrument in a state is precisely its expected value in the transition states. Assume a feasible point is found and recorded in a data file.