A Result on Integral Functionals with Infinitely Many Constraints

Abstract

A classic paper of Borwein/Lewis (1991) studies optimisation problems over L^p_+ with finitely many linear equality constraints, given by scalar products with functions from L^q. One key result shows that if some x in L^p_+ satisfies the constraints and if the constraint functions are pseudo-Haar, the constraints can also be realised by another function y in the interior of L^\infty_+ . We establish an analogue of this result in a setting with infinitely many, measurably parametrised constraints, and we briefly sketch an application in arbitrage theory.

Keywords: linear equality constraints, feasible solution, infinitely many constraints, random measure, arbitrage theory, equivalent martingale measures

JEL Classification: C60, C65, Z00