Nonnegative Wealth, Absence of Arbitrage, and Feasible Consumption Plans - Dybvig, Philip H.; Huang, Chi-Fu (Review of Financial Studies, 1988)
A restriction to nonnegative wealth is sufficient to preclude all arbitrage opportunities in financial models that have no arbitrage in limits of simple strategies. Imposing nonnegative wealth does not constrain agents from making the choice they would make under the standard integrability condition. These conclusions do not depend on whether markets are complete.