Admissible Trading Strategies under Transaction Costs

2013/08/07 by Walter Schachermayer, Schachermayer, Walter · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Economic theories and models #FOS: Economics and business #FOS: Mathematics #Pricing of Securities (q-fin.PR) #Probability (math.PR) #Risk and Portfolio Optimization #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1308.1492

openalex publication_date 2013/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A well known result in stochastic analysis reads as follows: for an ℝ-valued super-martingale X = (X_t)_{0≤ t ≤ 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⋅ S) verifying x+(H⋅ S)_T≥ 0 also satisfies x+(H⋅ S)_t≥ 0, for all 0 ≤ t ≤ 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.

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