Before revision:  We show that the RNUPBR condition on terminal liquidation value holds if and only if there exists a strictly consistent local martingale system (SCLMS) . Moreover, we show that RNUPBR condition implies the existence of optimal solution of the utility maximization problem defined on the terminal liquidation value .
After revision:  We show that the RNUPBR condition on terminal liquidation value holds if and only if there exists a strictly consistent local martingale system (SCLMS) . Moreover, we show that RNUPBR condition implies the existence of optimal solution of the NUPBR and NLABP conditions in the robust sense for the smaller bid-ask spreads is the equivalent characterization of the existence of SCLMS for general market models. As a consequence, the relationship between NUPBR and NLABP conditions in the robust sense and the market viability is examined. Moreover, different types of arbitrage opportunities with transaction costs are also discussed and the comparison between our setting and the frictionless market models is also presented .