Non-arbitrage for Informational Discrete Time Market Models

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.