Necessary and Sufficient Conditions for Weak No-Arbitrage in Securities Markets with Frictions

Abstract

In this paper we consider a financial market model with frictions which include transaction costs, bid-ask spread and taxes. By using optimization, linear and nonlinear programming and convex programming techniques, several necessary and sufficient conditions are derived for the weak no-arbitrage. Some results on state prices are also provided. The results of this paper can provide at least some theoretical insight to the problem.

Harnack Inequality and No-Arbitrage Analysis

“…Many articles have studied the no-arbitrage condition mainly by functional analysis, the Martingale approach, and convex optimization. These articles yield plentiful rich results [6][7][8].…”

Geometric No-Arbitrage Analysis in the Dynamic Financial Market with Transaction Costs

“…Furthermore, Jouini and Kallal (1995) characterized arbitrage in the market with bid-ask spreads by a martingale approach. Deng et al (2000Deng et al ( , 2005 considered the market with transaction costs and bid-ask spreads and then gave the no-arbitrage conditions by convex optimization theories and linear programming methods. Surprisingly, the arguments of differential geometry and Harnack inequality, etc., in recent years, are used to study some hot topics in a frictionless financial market.…”