Andrés CarvajalJohn GeanakoplosÁlvaro Riascos2026-03-222026-03-22200810.12660/bre.v28n22008.1513https://doi.org/10.12660/bre.v28n22008.1513https://andeanlibrary.org/handle/123456789/61335We provide a shorter proof than Geanakoplos and Polemarchakis (1986) of the existence of equilibrium in an incomplete financial market economy with numeraire assets, under the weak assumption that asset returns are non-negative. Furthermore, we relax the strict monotonicity assumption on preferences and as an application we prove the existence of equilibrium when agents may disagree on zero probability events but do not plan to go bankrupt in any state.enNuméraireIncomplete marketsMonotonic functionMathematical economicsAsset (computer security)EconomicsComplete marketZero (linguistics)General equilibrium theoryarticle