Arbitrage without borrowing or short selling?

TL;DR

This paper demonstrates that a trader with no initial wealth, no borrowing, and no short selling can achieve arbitrage profits through perfect foresight and continuous trading, highlighting complexities in defining self-financing in continuous-time models.

Contribution

It introduces a theoretical arbitrage strategy without borrowing or short selling, relying on perfect foresight and continuous trading, challenging traditional no-arbitrage assumptions.

Findings

A trader with perfect foresight can generate positive wealth without initial capital.

Arbitrage strategies can be constructed as finite variation processes satisfying self-financing conditions.

The paper highlights complexities in formulating self-financing conditions in continuous-time models.

Abstract

We show that a trader, who starts with no initial wealth and is not allowed to borrow money or short sell assets, is theoretically able to attain positive wealth by continuous trading, provided that she has perfect foresight of future asset prices, given by a continuous semimartingale. Such an arbitrage strategy can be constructed as a process of finite variation that satisfies a seemingly innocuous self-financing condition, formulated using a pathwise Riemann-Stieltjes integral. Our result exemplifies the potential intricacies of formulating economically meaningful self-financing conditions in continuous time, when one leaves the conventional arbitrage-free framework.