Admissible Trading Strategies under Transaction Costs

Abstract

A well known result in stochastic analysis reads as follows: for an $\mathbb{R}$-valued super-martingale $X=(X_t{)}_{0\le t\le T}$ such that the terminal value $X_T$ is non-negative, we have that the entire process $X$ is non-negative. An analogous result holds true in the no arbitrage theory of mathematical finance: under the assumption of no arbitrage, a portfolio process $x+(H\cdot S)$ verifying $x+(H\cdot S{)}_T\ge 0$ also satisfies $x+(H\cdot S{)}_t\ge 0,$ for all $0\le t\le T$. In the present paper we derive an analogous result in the presence of transaction costs. A counter-example reveals that the consideration of transaction costs makes things more delicate than in the frictionless setting.

Paper has been expanded by inserting section 2 The numéraire-free setting

Cited by in corpus (1)

• Asset Price Bubbles in market models with proportional transaction costs