Combination trading with limit orders

We model the exchange of commodities that are contingent upon each other, when traders place mostly limit orders. Examples include: (1) a market of financial futures where future spreads are also traded, (2) a market of mutual funds and stocks, (3) a market of options and stocks, under the viewpoint that they are both combinations of Arrow-Debreu securities. We prove that consistent prices are optimal. We develop a fixed-point algorithm to compute an optimal price and allocation. The algorithm combines ideas from contraction mapping theory and from homotopy theory. It is much faster than a traditional linear programming approach.