On the Market Viability Under Proportional Transaction Costs

34 Pages Posted: 2 Feb 2014 Last revised: 11 Apr 2016

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Xiang Yu

Hong Kong Polytechnic University - Department of Applied Mathematics

Date Written: April 11, 2016

Abstract

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

Bayraktar, Erhan and Yu, Xiang, On the Market Viability Under Proportional Transaction Costs (April 11, 2016). Available at SSRN: https://ssrn.com/abstract=2388757 or http://dx.doi.org/10.2139/ssrn.2388757

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Xiang Yu (Contact Author)

Hong Kong Polytechnic University - Department of Applied Mathematics ( email )

Yip Kit Chuen Building
Hung Hom
Kowloon
Hong Kong

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