A Fixed Point Theorem for Measurable Selection Valued Correspondences Induced by Upper Caratheodory Correspondences

Publication Date
Systemic Risk Centre Discussion Papers DP 115
Publication Date
Financial Markets Group Discussion Papers DP 850
Publication Authors

We show that any measurable selection valued correspondence induced by the composition of an m-tuple of real-valued Caratheodory functions with an upper Caratheodory (uC) correspondence has fixed points if the underlying uC correspondence in the composition contains a continuum valued uC sub-correspondence. Moreover, this composition of the m-tuple of real-valued Caratheodory functions with the continuum valued uC sub-correspondence induces a measurable selection valued sub-correspondence that is weak star upper semicontinuous.