Arbitrage and non-linear taxes

Incorporating a progressive income tax into an economic decision problem raises the question whether this tax does not create arbitrage opportunities. We investigate this problem in a riskless (multi-period) economy. With a convex tax function we identify a particular kind of arbitrage (called bounded arbitrage): In this case the gain achievable through arbitrage trade is limited and cannot reach infinity.We are able to give a complete characterisation based on prizes of the traded assets as to whether bounded as well as unbounded arbitrage opportunities will exist.