Non-arbitrage for Informational Discrete Time Market Models

2014/07/06 by Tahir Choulli, Jun Deng, Choulli, Tahir +1
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR) #math.PR #q-fin.MF

paper · pdf · doi:10.48550/arxiv.1407.1453

22 pages

arxiv created 2014/07/06 · arxiv updated 2014/07/08

Abstract

This paper focuses on the stability of the non-arbitrage condition in discrete time market models when some unknown information τ 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 τ 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.

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