In a discrete-time setting, we study arbitrage concepts in the presence of
convex trading constraints. We show that solvability of portfolio optimization
problems is equivalent to absence of arbitrage of the first kind, a condition
weaker than classical absence of arbitrage opportunities. We center our
analysis on this characterization of market viability and derive versions of
the fundamental theorems of asset pricing based on portfolio optimization
arguments. By considering specifically a discrete-time setup, we simplify
existing results and proofs that rely on semimartingale theory, thus allowing
for a clear understanding of the foundational economic concepts involved. We
exemplify these concepts, as well as some unexpected situations, in the context
of one-period factor models with arbitrage opportunities under borrowing
constraints.Comment: 29 pages, 1 figur