On the market viability under proportional transaction costs

2013-12-13

AI Summary

This paper identifies an error in a corollary of Theorem 2.8 in Bayraktar & Yu (2018), undermining their market viability conclusion under proportional transaction costs. To address feasibility, it proposes strict consistent local martingale systems (SCLMS) — replacing the conventional strict consistent pricing systems — as the dual criterion, and constructs a unified verification framework based on two weak no-arbitrage conditions: NUPBR (no unbounded profit with bounded risk) and the newly introduced NLABP (no local acceptable profit). It establishes, for the first time, the robust equivalence between SCLMS and both NUPBR and NLABP. The introduction of NLABP extends the scope of arbitrage-free theory to broader settings with transaction costs. Finally, the paper derives necessary and sufficient conditions for market viability under proportional transaction costs, providing a novel theoretical foundation for utility maximization in frictional markets.

Abstract

This paper studies the market viability with proportional transaction costs. Instead of requiring the existence of strictly consistent price systems 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 (NLABPs). In particular, we show that the NUPBR and NLABP conditions in the robust sense are equivalent to the existence of SCLMS for general market models. We also discuss the implications for the utility maximization problem.

Problem

• Identifying errors in Theorem 2.8 implications
• Weakening the original theorem's statement
• Correcting mathematical finance transaction cost analysis

Innovation

• Identifies errors in theorem
• Corrects mathematical finance implications
• Addresses proportional transaction costs