Non-arbitrage for Informational Discrete Time Market Models

TL;DR

This paper investigates the stability of the no-arbitrage condition in discrete-time market models when incorporating unknown information, providing conditions for its preservation and illustrating with explicit examples.

Contribution

It establishes necessary and sufficient conditions on unknown information to ensure non-arbitrage in any market, extending the understanding of market stability under information asymmetry.

Findings

Non-arbitrage condition preserved under mild market assumptions

Necessary and sufficient conditions on information for non-arbitrage

Explicit calculation of arbitrage opportunities when conditions fail

Abstract

This paper focuses on the stability of the non-arbitrage condition in discrete time market models when some unknown information $\tau$ is partially/fully incorporated into the market. Our main conclusions are twofold. On the one hand, for a fixed market $S$, we prove that the non-arbitrage condition is preserved under a mild condition. On the other hand, we give the necessary and sufficient equivalent conditions on the unknown information $\tau$ to ensure the validity of the non-arbitrage condition for any market. Two concrete examples are presented to illustrate the importance of these conditions, where we calculate explicitly the arbitrage opportunities when they exist.