International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 139690, 20 pages
Research Article

The Completion of Real-Asset Markets by Options

Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, Building B, Karlovasi, 83200 Samos, Greece

Received 2 April 2010; Revised 25 November 2010; Accepted 16 December 2010

Academic Editor: S. M. Gusein-Zade

Copyright © 2010 Christos E. Kountzakis. 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 combine the theory of finite-dimensional lattice subspaces and the theory of regular values for maps between smooth manifolds in order to study the completion of real asset markets by options. The strike asset of the options is supposed to be a nominal asset. The main result of the paper is like in the case of the completion of a nominal asset market by options that if the strike asset of the options is the riskless asset, then the completion of a real asset market is generically equal to 𝑆 .