Journal of Applied Mathematics and Decision Sciences
Volume 1 (1997), Issue 2, Pages 133-150

Combination trading with limit orders

Henry Schellhorn

Oracle Corporation, 604 Arizona Avenue, Santa Monica 90401, CA, USA

Copyright © 1997 Henry Schellhorn. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.