On the Market Viability Under Proportional Transaction Costs
34 Pages Posted: 2 Feb 2014 Last revised: 11 Apr 2016
Date Written: April 11, 2016
This paper studies the market viability with proportional transaction costs. 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 show 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. We also discuss the implications for the utility maximization problem.
Keywords: Proportional Transaction Costs, (Robust) No Unbounded Profit with Bounded Risk, Strictly Consistent Local Martingale Systems, (Robust) No Local Arbitrage with Bounded Portfolios, Utility Maximization, Market Viability, Numeraire Portfolios
JEL Classification: G11, G12
Suggested Citation: Suggested Citation