A Variational Problem Related to a Continuous-Time Allocation Process for a Continuum of Traders

Abstract

We provide an existence theorem to continuous-time allocation process for a continuum of traders, in the absence of a concavity condition on the utility function, and under the presence of some economic parameters. 

A pointwise constrained version of the Liapunov convexity theorem for single integrals

“…The multitude of potential applications of these results can easily be guessed by recalling all the research papers, using the Liapunov convexity theorem as main tool of the proof, which have been published on nonconvex ordinary differential inclusions, calculus of variations and optimal control, since the pioneering works [3,12], including, e.g., dozens of papers published by the last author of the present paper, along the last quarter of century, together with, e.g., [1,2,8,14,17,18].…”