Abstract
In this paper we propose a general mathematical approach to existence problems in economics based on the geometry of vector bundles and the methods of intersection theory. The existence problem is formulated as: Does an approximate vector bundle admit a non-zero continuous section? The motivation and major application comes from incomplete market theory, where the appropriate vector bundle has, as one of the components of its base space, a Grassmanian manifold. Several general existence results are offered. One infinite dimensional generalization is included.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.