We consider a notion of weak no arbitrage condition commonly known as Robust No Unbounded Profit with Bounded Risk (RNUPBR) in the context of continuous time markets with small proportional transaction costs . 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 .
This paper studies the market viability with proportional transaction costs in the sense that the utility maximization problems defined on terminal liquidation values admit optimal solutions. Instead of requiring the existence of strictly consistent price systems (SCPS) as in the literature, we show that strictly consistent local martingale systems (SCLMS) can successfully serve as the dual elements such that the market viability can be verified. We introduce two weaker notions of no arbitrage conditions on market models named no unbounded profit with bounded risk (NUPBR) and no local arbitrage with bounded portfolios (NLABP). In particular, we reveal that 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 .
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We consider a notion of weak no arbitrage condition commonly known as Robust No Unbounded Profit with Bounded Risk (RNUPBR) in the context of continuous time markets with small
This paper studies the market viability with
R
. We show that the RNUPBR condition
in the sense that the utility maximization problems defined
R
value holds if and only if there exists a strictly consistent local martingale system
values admit optimal solutions. Instead of requiring the existence of strictly consistent price systems (SCPS) as in the literature, we show that strictly consistent local martingale systems
R
. Moreover, we show that RNUPBR condition implies the existence of optimal solution of
can successfully serve as the dual elements such that the market viability can be verified. We introduce two weaker notions of no arbitrage conditions on market models named no unbounded profit with bounded risk (NUPBR) and no local arbitrage with bounded portfolios (NLABP). In particular, we reveal that
R
utility maximization problem defined on the terminal liquidation value
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