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 a market of nancial futures where future spreads are also traded a market of mutual funds and stocks 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 xed 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