Arbitrage and Non-linear Taxes

Incorporating a progressive or convex income tax into valuation problems raises the question of the appropriate tax rate to use in common valuation formulas. We apply arbitrage theory in a riskless, as well as risky, (multi-period) economy to answer this question. It turns out that the appropriate tax rate depends on the marginal tax rate of the investor's initial endowment.With tax liabilities that are a convex function of the tax base we identify a new kind of arbitrage: trading strategies where the gains from trades remain unchanged if this strategy is applied multiple times. We call these strategies ‘bounded' arbitrage opportunities.Going beyond earlier research, we are able to give a complete characterization based on properties of the tax liability function as to whether bounded as well as unbounded arbitrage opportunities will exist